Monotone operator theory and finite element analysis with remeshing algorithm is developed for study of elastoplastic behaviour of homogeneous materials under indentation. Convexity and continuity properties of the nonlinear functional related to plasticity operator is analyzed. In the considered formulation the problem is nonlinear even for physically linear (pure elastic) materials, since the unknown contact domain on each step of indentation is assumed to be unknown. Numerical algorithm presented is based on a locally adaptable mesh in order to find the unknown contact domain with high accuracy. Computational results show high predictive capability of the proposed model for indentation of inelastic homogeneous materials. (c) 2004 Elsevier Inc. All rights reserved.