The problem of a smooth circular punch penetrating an elastic half-space with a spherical cavity is considered. The solution, which accounts for the disturbances in the contact stress distribution under the punch due to the subsurface cavity, is carried out within the classical theory of elasticity. The mixed boundary-value problem is reduced first to a pair of dual integral equations, and then to an infinite system of simultaneous equations. The results are presented, illustrating the dependence of the contact stress disturbance upon the geometrical parameter of the punch.