Abstract An analytical model was developed for predicting the blast response of a double-curvature, composite sandwich shallow shell with PVC foam core. Based on Donnell’s nonlinear shallow shell formulation, the PVC foam core was modeled with isotropic and transversely isotropic elastic–plastic properties. The predicted transient response was shown to be in good agreement with Finite Elements (ABAQUS Explicit) when assuming isotropic foam crushing. For sandwich shells with higher curvature and in-plane membrane resistance, lower blast resistance was found with transversely isotropic than isotropic core crushing. This indicated that modeling the core of the sandwich shell as isotropic instead of transversely isotropic would give non-conservative estimates of the structure’s ability to resist blast loading for some sandwich shell geometries.