This paper presents a numerical study of the Lorentz force and fluid flow induced by a rotating magnetic field in a medium with a nonhomogeneous electric conductivity placed in a cylindrical vessel with insulated walls. The nonhomogeneity is modeled by the presence of a solid and a liquid phase of different electrical conductivity. The solid phase is located orthogonally to the axis of rotation, which corresponds to the case of unidirectional solidification. The simulations were performed for different locations of the solid front and different ratios of the electrical conductivity, σ_s/σ_l, = 0.2. ........ 10. Here σ_s, and σ_l are the electric conductivity of the solid and liquid phases, respectively. The results showed that the difference between electrical conductivity of solid and liquid phases has a noticeable effect on the mean-time Lorentz force and the velocity: namely, the presence of the solid phase (σ_s > σ_l) leads to an increase of the Lorentz force and fluid flow in the cylinder.