Within the frame-work of finite deformations of continuous media, the quasi-static deformations are considered that ensues upon applying internal pressure and axial shear stress, uniformly distributed along the surface of a cylindrical hole of infinitesimal initial radius in an elastic-plastic body of unbounded extent. With internal pressure only, also dynamic effects are taken into account. For each considered case of material and loading analytic expressions are given for the state of stress in the body and the amount of energy being dissipated in plastic working during the deformation process. The obtained results furnish the basis for a discussion of the influence of material parameters on the mechanical behavior of armor materials.