The calculation of nonhydrostatic stresses in the interior of Mars is carried out without taking into account the long-wave component. The numerical solution of the system of equations of elastic equilibrium for a gravitating planet was carried out on a grid with a resolution of 1° × 1° in latitude and longitude. Data on the topography and gravitational field of the planet, starting with the seventh harmonic, were used as boundary conditions. Most of the epicenters of marsquakes are located in zones of extensions and sufficiently large tangential stresses arising as a result of the planet’s deviation from the state of hydrostatic equilibrium. The directions of the main stress axes and their correspondence to the strike of geological structures on the planet’s surface are given.