||This article describes distributions of stresses and strains created by pressing a ball with 80 HRC hardness into soft 35HRC steel, which occurs in the technological process of burnishing. We present a computer model and a solution developed with the Nastran FX program, based on the finite elements method. The validity of the model has been checked using a small force applied on the ball, within the range of elastic deformations, where Hertz formulas are applicable. Then computations have been made for a pressure force of 30 000 N, which corresponds to hardness testing conditions by the Brinell method. The dimensions of plastic indentations from simulations and experiments are compared.