The stress system in a semi-infinite elastic solid with given normal surface loading is of importance in many problems of machine and structural design and strength of materials. It often happens in such cases that the stresses in which one is primarily interested are those in the surface of the body. This paper presents some observations that can be made regarding the stresses and displacements in the surface.

Typical objectives of structural design and typical constraints in rheology are discussed and classified. They are divided into two groups: the objective may depend on time (creep velocities, creep displacements, stress relaxation), or may be independent of time (time to rupture, critical time in creep buckling problems). The optimal shape may be either constant in time (called here “absolute optimum”), or a function of time (temporary optimum). The latter case is of restricted engineering interest; the notion of “engineering optimum” is here introduced (constant shape, not strictly optimal). Several problems are treated in detail.