We analyze nonhydrostatic stress field in the Martian interior for two types of heterogeneous elastic models: the ones with a lithosphere and the ones with a lithosphere and probable melting zones within it. Numerical modeling of the system of elastic equilibrium equations for a gravitating planet is carried out on a 1 × 1 arc degree spherical grid down to a depth of 1000 km. The boundary conditions are specified by the topography and gravity field data determined relative to a hydrostatic equilibrium spheroid taken as the ref- erence surface. High maximum shear stresses in the zones of high tensile stresses are assumed as the criterion for selecting the probable marsquake sources. Irrespective of the type of rheological model, the zones of the high shear and tensile stresses in the crust and mantle of the Mars arc revealed beneath Hellas Planitia, Argyre Planitia, Mare Acidalia, Arcadia Planitia plain, and Valles Marineris.