Should  we be able fast like the fasts described in Bible? If you look carefully at the scripture, there are instances were some people fast to pray and/or to express their sorrow. However, the length of the fast seems to be  astronomical; some people like Moses has fasted for about 40 days:


  Exodus 34:28: 28 Moses stayed there with the Lord forty days and forty nights, and during that time he did not eat food or drink water. And Moses wrote the words of the Agreement—the Ten Commandments—on the stone tablets.


And Jesus also fasted for about same length of time:


  Matthew 4:1-2:  1 Then the Spirit led Jesus into the desert to be tempted by the devil. 2 Jesus fasted for forty days and nights. After this, he was very hungry. 


Is it physically possible for us to do the same? I sincerely doubt that most people would die before 25 days.
Strictly medically speaking... Depending on your health, and the amount of stored body fat/muscle mass that you have when beginning to fast, it is physically possible to fast for more than 40 days.

Per this article: http://health.howstuffworks.com/diseases-conditions/death-dying/live-without-food-and-water1.htm


  Medically speaking, most doctors agree that healthy humans can go up
  to eight weeks without food as long as they have water. People have
  gone longer and been fine, and people have starved to death in less
  time. Being strong and in good physical shape can help you survive
  longer, but so does having extra body fat. The body stores energy
  needed to live in the form of fat, carbohydrates and proteins. The
  carbs are the first thing to be used up without more food coming in.
  The fat goes next, which explains why people with more of it can
  survive longer. Then the proteins go. If you get to the point that
  your body is using up proteins, basically the body itself, then you're
  in bad shape.


Eight weeks comes out to 56 days, of course, which is above and beyone even the 40 days you mentioned.

As for going without water for this time period, medical science says no, we can't live nearly that long.  

The same article says this on the next page:


  Assuming you're in reasonable shape and in ideal conditions -- that
  is, not in the heat or cold and not exerting, a human can probably
  live for about 3 to 5 days without any water. Healthier humans can
  live another day or so longer.


However, Moses likely had divine intervention.  Of course, that can't be proved outside of the Biblical account, so that would make the question unanswerable using objective criteria.