The development of the model of the multistep nanoindentation test with Berkovich indenter, accounting for the residual stress distribution, is one of the aims of the present paper. The specimen is unloaded in the intervals between the deformation steps. Substrate, which is composed of a ferritic steel and biocompatible pulsed laser deposition TiN coating, is considered. The selection of the TiN was inspired by its perspective application as the coating for a constructional element of the heart prosthesis (blood chamber and aortic valves). Sensitivity analysis of the model predictions with respect to its parameters is presented in the present paper. The theory of elastic-plastic deformations is used in the finite element model, which simulates both loading and unloading phases, accounting for the real geometry of the indent. The main goal of the present paper was to inversely analyse the tests for coating/substrate system. Square root error between measured and predicted forces is the objective function in the analysis. Results of the inverse calculations, which are presented in the present paper, may be helpful in simulations of the behaviour of TiN deposited on substrate in various applications as bionanomaterials.