We present results of atomistic computer simulations of solid-liquid interfaces when the solid is subject to non-hydrostatic stresses. The methodology includes molecular dynamics simulations, the semi-grand canonical Monte Carlo method and embedded-atom potentials. A generalized adsorption equation and various thermodynamic integration schemes are applied to study the effect of applied lateral stresses (uniaxial, biaxial, tension, compression, etc.) on the interface stress, interface free energy, segregation and other thermodynamic properties. As expected from thermodynamic relations, the shift of the solid-liquid equilibrium temperature is found to be quadratic in non-hydrostatic components of the stress tensor in the solid. At a critical value of the lateral compression stress, the interface loses stability and triggers rapid crystallization into stress-free solid, leaving a relatively sharp stressed/unstressed solid/solid interface behind.