In this work we solve the Barker-Ferry equation which accounts for the quantum character of the electron-phonon interaction in semiconductors in the framework of the Monte Carlo (MC) method. The first part of the work considers the zero electric field formulation of the equation in spherical coordinates. Different MC algorithms for solving the equation are suggested and investigated. In the second part of the work we consider the case of an applied electric field. It is shown that the second algorithm from the first part can be successfully modified to account for the cylindrical symmetry of the task.