The foam materials, by construction and by characteristic properties (low density, large deformations, great flexibility, Poisson ratio practically zero etc.), are widely used in many and various domains. The numerical simulation of the foam material behavior raises some difficulties, which can be impassable under certain circumstances. This paper presents some of our researching results in numerical modeling of foam materials, which can be very useful for those interested in numerical modeling of the foam materials. Numerical modeling used by the authors is based on the finite element method (FEM) and on the element-free Galerkin (EFG) method. The results are presented in a comparatively way and they also present how some usually running errors can be avoided. The conclusions and the results are considered by the authors very useful in modeling of the foam materials and in choosing of the most fitted method too.