According to many experimental investigations of porous chalk an elastoplastic model with two yield surfaces is proposed. The physical meaning of the parameters of the model and the method used for their determination are explained. Some laboratory tests are then simulated in order to validate the model. Hydrostatic compression tests are performed using different kinds of saturating fluid. The chalk responses obtained can be classified into two groups corresponding to two groups of fluids : water and oil. The dependency of chalk behaviour with saturating fluid is explained through the capillary effect and "wettability" of the fluid. A new approach for numerical modeling is proposed it is assumed that there are two chalk materials, oil and water saturated, superposed on the same material point. Some validation examples are presented.