We present a suite of analytical and semianalytical solutions for the displacements, strains, and stress due to distributed anelastic deformation of finite strain volumes in a half‐space for cuboid sources. We provide the solutions in the cases of antiplane strain, plane strain, and 3D deformation. These expressions represent powerful tools for the analysis of deformation data to image distributed strain in the Earth’s interior and for the dynamic modeling of distributed deformation off faults, including thermoelasticity, poroelasticity, and viscoelasticity. We include computer programs that evaluate these expressions free of major singular points. Combined with formulas that describe the deformation around faults, these solutions represent a comprehensive description of quasi‐static deformation throughout the earthquake cycle within the lithosphere–asthenosphere system.