Question

why artery walls are very strong and elastic?

Answer 1

because artery carries the blood from heart which is pure and it has to travel faster so it exerts more pressure on the wall. this is the reason why artery walls are strong and elastic.

Answer 2

The walls of an artery are muscular because they have to maintain some pressure to keep the blood flowing at a steady rate. The artery is delivering oxygen to the cells, and this needs to be precisely regulated. 
The vein is mainly returning blood to the heart. It may be carrying food to the cells and waste to the kidneys and lungs; but this doesn't require as much precision in terms of speed. Not needing the muscles, the walls are thinner.

Hope this may helps u..........