A numerical method is used to resolve the classic Mindlin-Cattaneo par
tial slip problem for contact between similar and between dissimilar b
odies. It is shown that, for similar bodies, the surface frictional en
ergy dissipation is concentrated off the plane of symmetry although th
e overall dissipation is similar to that predicted by the classical so
lution. This effect is enhanced for certain combinations of dissimilar
materials, where the process of frictional shakedown leads to a displ
aced contact and hence additional shear compliances.