As others have said, you cannot use beamerarticle with the beamer class. Compile interactively or look at the log/output to see the errors this produces. You can ignore these and get a PDF but things are going to go awry in subtle, and not so subtle, ways if you do that. Besides, there are better options:
Handout Mode
Here is the effect of using beamer's handout mode:

That is, all slides on a frame are 'flattened' to produce a single snapshot of the completed frame.
The Code
\documentclass[handout]{beamer}
\usepackage{tikz}
\begin{document}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[red, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\end{document}
Article Mode
If you want to produce a more traditional handout which doesn't look like slides at all, you can use beamerarticle, as others have pointed out, with the class of your choice. For example:

The Code
\documentclass{article}
\usepackage{beamerarticle}
\usepackage{tikz}
\usepackage{kantlipsum}
\begin{document}
\mode<article>{
\section{This is only in the article}
\kant[1]
}
\section{In all modes}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[red, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\end{document}
Presentation Mode
Note that replacing the article class with beamer and commenting \usepackage{beamerarticle} puts you in 'regular' beamer mode with all the bells and whistles used in presentations. That is, essentially the same code:
% \documentclass{article}
\documentclass{beamer}
% \usepackage{beamerarticle}
\usepackage{tikz}
\usepackage{kantlipsum}
\begin{document}
\mode<article>{
\section{This is only in the article}
\kant[1]
}
\section{In all modes}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[red, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\end{document}
produces quite different output:

Handout Mode Revisited
One problem with the standard handout produced by beamer is that it is not very efficient in terms of paper. If your presentation has 10 or 20 slides, you do not really need 10 or 20 pages in your handout. The solution suggested in the manual is to use pgfpages which avoids the need for a separate source file. This allows you to display several frames on one page. Suppose, for example, you have four frames rather than one in green, blue and yellow as well as red. In conjunction with handout mode, pgfpages allows you to produce something like this:

The Code
% \documentclass{article}
\documentclass[handout]{beamer}
% \usepackage{beamerarticle}
\usepackage{tikz}
\usepackage{kantlipsum}
\usepackage{pgfpages}
\pgfpagesuselayout{4 on 1}[a4paper,border shrink=5mm,landscape]
\pgfpageslogicalpageoptions{1}{border code=\pgfstroke}
\pgfpageslogicalpageoptions{2}{border code=\pgfstroke}
\pgfpageslogicalpageoptions{3}{border code=\pgfstroke}
\pgfpageslogicalpageoptions{4}{border code=\pgfstroke}
\begin{document}
\mode<article>{
\section{This is only in the article}
\kant[1]
}
\section{In all modes}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[red, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[red, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[blue, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[blue, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[blue, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[green, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[green, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[green, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\begin{frame}[plain]
\begin{tikzpicture}
\draw[yellow, very thick] (0.35, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[yellow, very thick] (1.65, -5.35) ellipse (0.6cm and 0.25cm);
\pause
\draw[yellow, very thick] (3.7, -5.25) ellipse (0.9cm and 0.3cm);
\end{tikzpicture}
\end{frame}
\end{document}
Other Options
There are other possibilities. For example, if you don't mind having an additional source file, you can use pdfpages rather than pgfpages to put multiple frames on a single page. (This is the option I tend to use most for handouts.)
Moreover, you can load a different theme to produce your handout e.g. one suitable for printing on a black-and-white printer or for photocopying.
beamerorbeamerarticleoutput? – Juri Robl Mar 05 '14 at 15:10LyXfor mybeamerslide. Then I usebeamerarticleinLyXto make handouts. I want to stick with this protocol because I'm lazy user ofLaTeX. Now I'vetikzcode in mybeamerwhich works fine but the same code throws error withbeamerarticle. If I delete\pausestatement, every thing works fine. – MYaseen208 Mar 05 '14 at 15:17pdflatexit doesn't work withbeamer+beamerarticle, because they try to declare the same commands. MaybeLyXis doing something different internally? – Juri Robl Mar 05 '14 at 15:21\pausecommands - I didn't test with them uncommented). Clearly a Bad Idea. But I can see why it might appear to work if LyX doesn't make the complaints obvious and/or you don't pay much attention to them. (I don't know if LyX does this or not.) – cfr Mar 06 '14 at 01:46\gdef\pause{\relax}after\begin{document}. Note that doing this is a terrible idea and you will still get error after error after error. You should use one of the solutions provided bybeamerspecifically for making handouts. Really. But this will get you a 'flat' result. What else it will do I am not prepared to even guess. Or put\RequirePackage{beamerarticle}before\documentclass. This is just as ugly and will produce equally horrible errors but will also flatten things. – cfr Mar 15 '14 at 03:48\let\pause=\relaxmay be better, as in contrast to\gdefit is not expanded on every call. It may save you some milliseconds. – Henri Menke Mar 15 '14 at 10:31\gdefwhen it didn't work. But I think it was because I had it in the wrong place initially. – cfr Mar 15 '14 at 15:32\global\let\pause=\relaxif you're unsure of grouping in a particular case. – Henri Menke Mar 15 '14 at 18:03\begin{document}. – cfr Mar 15 '14 at 18:56\pauseis defined in\AtBeginDocumentor things like that. Then all efforts are futile.:-)(This is my last comment. I don't want to exaggerate the discussion.) – Henri Menke Mar 15 '14 at 19:28