Two problems on phase transitions in a continuous medium are considered. The first problem deals with an elastic medium admitting more than two phases. Necessary conditions for equilibrium states are derived. The dependence of equilibrium states on the surface tension coefficients and temperature is studied for one model of a three-phase elastic medium such that each phase has a quadratic energy density. The second problem deals with phase transitions under some restrictions on the vector field under consideration. These restrictions imply that this vector field is solenoidal and its normal component vanishes on the boundary of the interfaces of phases. The equilibrium equations are deduced.