Numerical studies of non-local plasticity effects on different materials and problems are carried out. Two different theories are used. One is of lower order in that it retains the structure of a conventional plasticity boundary value problem, while the other is of higher order and employs higher order stresses as work conjugates to higher order strains and uses higher order boundary conditions. The influence of internal material length parameters is studied, and the effects of higher order boundary conditions are analyzed. The focus of the thesis is on metal-matrix composites, and non-local effects on various plane strain problems subject to different boundary conditions; but also void growth, steady-state crack propagation, and wire torsion are studied. In the thesis different non-local plasticity theories are compared, and some aspects on the mathematical character of a lower order theory is discussed.