In this paper, numerical solutions are presented for the MHD flow in a pipe surrounded by an electrically conducting medium, and under the influence of a transverse magnetic field. The boundary element method is used which discretizes only the pipe wall and is suitable for the infinite exterior region. Coupled MHD equations for the velocity and induced magnetic field inside the pipe, and the induced magnetic field equation for the outside medium are solved simultaneously taking into account also coupled boundary conditions on the pipe wall for exterior and interior magnetic fields. The boundary integral equation in the exterior region is restricted to the boundary of the pipe due to the regularity condition at infinity. Numerical results indicate that the coupling of BEM approaches for inside and outside regions has the ability to produce satisfactory results even the ratio of fluid magnetic Reynolds number to external medium magnetic Reynolds number reaches to 500. Computations are also carried out for different Reynolds numbers and values of magnetic pressure of the fluid in the pipe.