A combined experimental and computational study is undertaken to measure the damage tolerance of sandwich composite structures, to understand their damage modes and failure mechanisms, and to develop predictive models for residual compressive strength. The study is performed on specimens of aluminum honeycomb core with eight ply quasi-isotropic, graphite/epoxy face sheets. Damage at the visible detection threshold is induced through quasi-static indentation of 25.4 and 76.2 mm diameter spheres. Compression tests of undamaged and damaged samples are performed for a range of layups and core densities. Results show that residual strength is sensitive to combination of face sheet and core properties, to the indentation damage type and extent, and to the observed failure mode. A finite element model is developed using Abaqus®/Explicit to simulate quasi-static indentation and compression after impact tests. The aluminum honeycomb core geometry is modeled explicitly using elastic-plastic shell elements, and validated against core crushing experiments. The predicted residual dent profiles show that the model successfully captures the mechanics of core crushing during indentation. However, the residual strength is over-predicted based on simulation of compression after impact. Future work will incorporate evolution of face sheet damage due to indentation and compressive loading.