Rigid, closed-cell, polyurethane foam consists of interconnected polyurethane plates that form cells. When this foam is compressed, it exhibits an initial elastic regime, which is followed by a plateau regime in which the load required to compress the foam remains nearly constant. In the plateau regime, cell walls are damaged and large permanent volume changes are generated. As additional load is applied, cell walls are compressed against neighboring cell walls, and the stiffness of the foam increases and approaches a value equal to that of solid polyurethane. When the foam is loaded in tension, the cell walls are damaged and the foam fractures. A constitutive theory for rigid polyurethane foam has been developed. This theory is based on a decomposition of the foam in two parts : a skeleton and a nonlinear elastic continuum in parallel. The skeleton accounts for the foam behavior in the elastic and plateau regimes and is described using a coupled plasticity with continuum damage theory. The nonlinear elastic continuum accounts for the lock-up of the foam due to internal gas pressure and cell wall interactions. This new constitutive theory has been implemented in both static and dynamic finite element codes. Numerical simulations performed using the new constitutive theory are presented.