Local facesheet buckling of a curved sandwich panel subjected to external pressure pulse loading was investigated in this paper. Equations of motion for the facesheet transient deformations in the sandwich shell were derived from Lagrange’s equations of motion, and solutions using this approach compared well with FEA results from ABAQUS Standard. Both facesheet fracture during stable deformation response and local dynamic pulse buckling of facesheets were considered as possible modes of failure in the curved sandwich panel. Parametric studies indicated that local facesheets buckling is more likely to occur than facesheet fracture in thin and deep curved sandwich panels. The facesheet laminate layup can also be adjusted to improve the local buckling resistance of the curve panel.