No. It is not possible for us to fast without food and water for fourty days in normal circumstances.
I will explain the answer as below. I base my answer on 'Celebration of Discipline' by Richard Foster.
In Bible the normal means of fasting involves abstaining from all food, solid or liquid, but not from water. In the forty day fast of Jesus (Luke 4), we are told that '
He ate nothing during those days
Luke 4:2a (NIV)
and toward the end of fast, he was hungry.
and at the end of them he was hungry. Luke 4:2b (NIV)
This indicates that he was abstaining from food, not water. I believe this is what usually involved in a fast.
We can see partial fasts as well
I ate no choice food; no meat or wine touched my lips; and I used no
lotions at all until the three weeks were over. Daniel 10:3 (NIV)
Also we can see some instances of absolute fast.
“Go, gather together all the Jews who are in Susa, and fast for me. Do
not eat or drink for three days, night or day. I and my attendants
will fast as you do. Esther 4:16
Here we see fast as 3 days and nights without even water.
Paul also fasted this way immediately after his encounter with Christ.
For three days he was blind, and did not eat or drink anything. Acts 9:9 (NIV)
Generally it is accepted that human body cannot go without water much more than three days. That would mean both Moses and Elijah would have engaged in supernatural fast in their fast as described in Due 9:9 and 1 King 19:8
I went up on the mountain to receive the tablets of stone, the tablets
of the covenant that the LORD had made with you, I stayed on the
mountain forty days and forty nights; I ate no bread and drank no
water. (Due 9:9)
So he got up and ate and drank. Strengthened by that food, he traveled
forty days and forty nights until he reached Horeb, the mountain of
God. 1 King 19:8
In both these cases we can see that a divine intervention in their life. So I believe we also should not undertake any supernatural fast, without clear command from God personally to us. So you are right, we should not undertake absolute fasts for more than 3 days unless God asks you to do so.
Now many who practiced fasting regularly starting with a meal or two and extended over time, say that fasting from food for fourty days is possible. (Source: Celebration of Discipline)