We consider an isochemical, isentropic, incompressible fluid half-space and study quasistatic viscoelastic perturbations, induced by two-dimensional surface loads, of a hydrostatic initial state. In view of the regional or local scale required for deformations of planets to be amenable to the half-space approximation, the model is assumed to be externally gravitating. We derive analytic solutions for the displacement and incremental stress components and study several approximations to the expressions. Particular emphasis is placed on discriminating between the material and local incremental stresses. Based on this distinction, new insight is gained into the physical significance of the solution.
