Stretching model to fit curve?

I’m trying to make a long cylinder deform along a nurbspath curve, kind of like a snake.

But the problem is the cylinder does not stretch to fit the end of the curve, and I can’t find out how to do it.

Can anyone help me?

For the curve set the Fill setting to ‘Full’ and set bevel depth and resolution

For the curve use another curve in the bevel object setting to set the cross section