In this paper, the authors present the results of software verification for solving magnetohydrodynamic problem in duct exposed to constant magnetic fields. The proposed approach uses the following open source software: OpenFOAM for solving problems of continuum mechanics using the finite volume method, Elmer for solving magnetic field distribution based on the finite element method, and EOF-library for data exchange between these two programs. The verification results were demonstrated by fluid flow in a square duct exposed to constant uniform spanwise magnetic field. The research was carried out with a laminar fluid flow, which makes it similar to the Hartmann's problem. The existing experience of calculating such problems, their verification and application were discussed. The paper provides a brief mathematical description of the proposed solution and basic procedures for implementing the code proposed by the authors. At the first stage of verification, the comparison of fluid velocity distribution results at Hartmann’s numbers equal to 1, 10, 20 and 50 was demonstrated. These results were obtained by means of proposed software, an analytical solution, and a test problem provided by OpenFOAM developers for two-dimensional case. At the second stage of software verification, sufficient convergence of the results was shown for fluid velocity distribution in the three-dimensional case of the Hartmann’s problem compared with the OpenFOAM test problem data and the results obtained by Comsol Multiphisics and ANSYS. As a result, distributions of the fluid flow velocity between Hartmann’s walls were obtained for various study cases: a two-dimensional problem, a three-dimensional problem with electrically insulated walls, and a three-dimensional problem with walls having infinite electrical conductivity. The last stage of the study corresponds to assessing of software performance in comparison with the built-in OpenFOAM solver and commercial software Comsol Multiphysics and ANSYS. It was found that the proposed approach takes more time to calculate these problems than the built-in OpenFOAM solver, but less than Comsol. However, the problem formulation in EOF-library allows solving problems with complex geometry, which is not available in the built-in OpenFOAM solver. In conclusion, analysis of computation performance with parallelization was carried out. It showed significant reducing of computation time with the help of EOF-library in comparison with the commercial software Comsol and ANSYS.