This thesis presents a new constitutive model for closed-cell foams tailored for compressive shock loads and an experimental investigation of two commercial foam products. The new model requires just two characterization experiments to find material parameters, making it far more convenient than other approaches. A specific form of the hyperelastic free energy function is developed that permits an extension of a three-phase composite theory to finite strain hyperelasticity providing the following advantages: 1) identification of the hyperelastic free energy contributions associated with the gas and material phases, 2) elimination of deviatoric experiments for parameter determination, and 3) proper behavior at the densification limit. A viscoelastic model of the matrix shear modulus is used to introduce rate effects and plasticity. A time-incremental formulation of the constitutive model is developed and implemented using a finite element approach. Model results are compared with data obtained in high strain-rate experiments.