Analytical solutions were derived for the transient response and damage initiation of a foam-core composite sandwich panel subjected to blast loading. The panel response was modeled in two consecutive phases: (1) a through-thickness wave propagation phase leading to permanent core crushing deformations and (2) a transverse shear wave propagation phase resulting in global panel deflections. The predicted transient deformation of a sandwich panel consisting of E-glass vinyl ester facesheets and H100 PVC foam core compared well with ABAQUS predictions. Analytical predictions of the critical impulse for damage initiation in several foam sandwich panels also compared well with ABAQUS predictions.