In this paper an attempt is made to use a shell theory that includes transverse normal stresses to study the contact–impact behaviour involving thick shells. The problem is solved using the finite element method. The contact criterion is imposed by means of displacement and force constraints. The Lagrangian multipliers technique is used to impose these constraints. The case of a spherical shell impacting a rigid wall with a constant velocity is considered for the analysis. It is shown that the method produces accurate results with less amount of computation than the usual three‐dimensional analyses. The effects of the thickness of shell, velocity of impact and modulus of the material are studied. Copyright © 1994 John Wiley & Sons, Ltd