Results are given for the contact law and state of stress induced in the co
ntact resulting from application of a pressure distribution on a double-lay
ered half-plane, or its indentation by a body of prescribed shape. The geom
etry is representative of that found widely in biomedical applications, par
ticularly the knee prosthesis, and also in more general engineering problem
s. The solution is given in a numerically efficient form, and the stress st
ates at the surface and within the structure that are associated with a num
ber of different combinations of materials are displayed.