A review of the uniaxial compression test on brittle solids is presented. The discussion focuses on the description of the post-peak behavior, where strength softening and fractures propagating mainly in the axial direction are observed. Based on experimental evidence and dimensional analysis, the post-peak axial stress is seen as a function of the axial displacement normalized by the radius of the specimen, and not of its height. Accordingly, a continuum theory of stress diffusion is developed that is able to account for size effect. As a practical application of the theory, the bearing capacity of a pillar in a deep mine is considered.