We present a very general geometrical correction method for enforcing collisions and other geometrical constraints between polygonal mesh surfaces. It is based o a global resolution scheme that takes advantage of an efficient use of the conjugate gradient algorithm to find the appropriate displacement of the mesh vertices that would satisfy all the constraints simultaneously, and according to momentum conservation laws. This method has been implemented in a cloth simulation system along with a collision response model that enforces a minimum “thickness” distance between cloth surfaces, which can be efficiently integrated in a simulation scheme based on implicit integration. Some provided examples illustrate the efficiency of the method.