Infinitesimal indentation by an axisymmetric rigid punch pressed normal to the plane boundary of a compressible, isotropic, elastic half-space subject initially to a uniform, finite deformation by a hydrostatic stress in planes parallel to the surface is studied to determine the influence of the material response, the initial finite deformation, and the punch geometry on both the incremental normal-stress distribution and the total applied indentation pressure. It is shown that the incremental stress distribution at the punch face is a function of the total applied normal force and the indentation geometry alone, and this leads naturally to a weak universal relation for a flat-ended punch. It is found that there exists an all-around hydrostatic plane stress at which the free surface is unable to support any normal indentation disturbance, however small; this collapse condition is identified as a surface instability phenomenon. The general reduction to the well-known classical solution is demonstrated for every isotropic elastic material. Details of the general analysis are illustrated for isotropic, hyperelastic Hadamard materials and several theorems are provided for this special situation. It is shown in each instance that the solution includes as a special case results derived elsewhere for incompressible, hyperelastic bodies in general, and for Mooney–Rivlin materials in particular; but the methods used here are totally different.