Unexpected expansion can be a cause of damage in quasi-brittle materials such as concrete, fired clays or rocks. Such expansions can be due to chemical reactions (alkali-silica reaction – ASR, sulfate attack) or physical phenomena (frost, transport of fluids). Expansion is caused by two main mechanisms: matrix deformation due to the pressure initiated by the formation of new phases in the porosity of the material, and matrix cracking, which increases the apparent swelling of the matrix. In this work, a poromechanical model is proposed to reproduce expansion in materials resulting from single or multiple pressures. In this model, plastic deformation is used to represent permanent strain due to diffuse cracking induced by the pressure. In the case of expansion in quasi-brittle materials, the permanent deformations induced by the pressure are anisotropic to take account of the impact of the initial material anisotropy and stress anisotropy on cracking. The model is then coupled with a damage model and used to evaluate the opening of localized cracks due to a pressure gradient in a laboratory specimen.