Abstract In the present part, higher-order and conventional first-order shear deformation theories in conjunction with nine-noded quadratic isoparametric Lagrangian elements are used to develop a finite element analysis procedure for studying the impact response of composite sandwich shells. The shell behaviour is based on the Donnell's shallow shell theory. The face thicknesses are assumed to be small compared to that of the core. For the computation of local indentation, the core beneath the impacting point is assumed to behave like an elastic foundation and is modelled employing twenty-noded isoparametric orthotropic brick elements. Numerical results are presented in the second part of the present paper.