The elastic properties of polymethacrylimide (PMI) foams were investigated experimentally and numerically. Standard tests were carried to measure the mechanical properties of ROHACELL(A (R)) WF and RIST grades foams. The tetrakaidekahedral unit cell was adopted to generate a 3D representative volume element (RVE) for the microstructure of PMI foams. It is assumed that the RVE represents the foam within the framework of elasticity. The RVE models thus created were analyzed with periodic boundary conditions to obtain the elastic properties of PMI foams by using finite element analysis (FEA). The numerical results were compared with the experimental data and the prediction of existing theoretical models, and the proposed model was found to give the best prediction for the effective modulus of PMI foams. Parameter studies were also carried out using the RVE models to investigate the effect of the foam cell size and cell thickness on the effective modulus of PMI foams.