The paper reports results of a numerical analysis of the wedge indentation problem. The main objective of this research is to investigate the influence of the lateral confining stress σ0 on the development of the plastic zone under the indenter and on the initiation of tensile fractures. Numerical analysis indicates that the location of maximum tensile stress (interpreted as the point of crack initiation) moves away from the indentation axis as the lateral confinement increases. It is found that a small increase in the confining stress from zero induces a large increase in the inclination of this point on the indentation axis. However, the confinement does not reduce significantly the maximum tensile stress and it hardly influences the indentation pressure. These numerical results shed some light on the mechanism of formation of lateral or sub-horizontal tensile cracks observed in the indentation experiments.