The thesis is divided into four main parts; a study of static and dynamic oblique indentation by spherical projectiles - and its relevance to the shot-peening process, a study of the mechanics and of the parameters affecting the shot-peening process, multiple impact erosion as related to the shot-peening process and explosive hardening as compared with the shot-peening process. In the first part, force-indentation curves are presented for the penetration of the plane surface of a nominally semi-infinite block by a round body; different metals were penetrated at different inclinations and under static conditions. These experimental results are compared with those Obtained from a simple theoretical model. Experiments were carried out to determine how the shape and extent of the plastically deformed zone varies with the relative obliquity of the metal surface and indenter. A newly devised method was also employed for investigating the obliquity of the load upon the plastically deformed zone in aluminium, alloy. Upper bound solutions were proposed to determine the effect-of the'obli4uity of the load applied: to a cylindrical punch for penetrating soft metals upon the average indentation pressure. A simple slip-line field, was assumed to apply for use in the case of Spherical punch indentation to determine the depth of the plastic zone. The study was extended further to cover the determination of the strain - distribution in soft metals when indented by rigid spherical and cylindrical punches driven obliquely into the flat surface at various angles. These distributions were obtained using a computer aided visioplasticity technique. A finite element mesh which utilizes a quadratic function and uniquely defines the displacement vector within each element was used. An Almansi strain tensor, which uses the instantaneous co-ordinates to determine the' strains was used for calculating large plastic 'strains. In the dynamic indentation, studies., a simple model is presented' for investigating the impact at--different angles of incidence of a rigid sphere against a block of relatively soft' material with a wide range of impacting speeds.