Elastic contact between a thick shell of revolution and a rigid plate in the case when the plate is brought into contact with the shell by giving a finite displacement to the plate is analysed by the finite‐element method. Field‐consistent higher‐order strain‐displacement relations with vanishing shear stresses on the surfaces are used. A finite element based on these relations is developed and used for the analysis. The contact conditions are imposed by use of the Lagrangian multipliers method, and the resulting minimization problem is solved iteratively. This procedure will lead to reduced memory requirements and computation time. Copyright © 1993 John Wiley & Sons, Ltd