Help modeling 3d vector field

I'd like some help in finding the correct mathematical description of the stuff below:

A sheet is deformed by a mass on it (like in one of those pictures showing the effects of General Relativity). Note: I said "mass", but it is not actually a mass, it's a (positive) scaler. This mass is applied in a point (as in gravitation).

More, the "force" applied by the "mass" should be normal to a plane beneath (the z=0 plane), and someway vary with the square of the distance to that plane. So, unlike gravity, this should be "point-to-plane", not "point-to-point".

The sheet should have some sort of "elastic module" (or "strain module", or something like that), so I can vary the value of the partial derivatives in a zone close to the "mass".

The field should vary from a maximum (N) to a minimum (0) and must always be positive. Of couse, the mass should vary from 0 to a maximum (m).The maximum value of the field should be where the "mass" "gets" the z=0 plane (so, when mass=m), and the minimum when the mass is zero.

Finally, the field should include a constant (like G for gravitation) to set up the field strength.

Please, explain what you are going to do, so I can understand everything. I'm not very expert in vector fields - really, I'm a student of Computer Science. I need it to develop an algorithm. It's NOT an homework! Of course, I feel a little confused about this stuff. I hope my description is clear.

Thank you in advance (and sorry for poor english! :) )