In this study, we have considered the Magnetohydrodynamic (MHD) flow in a pipe with a circular or square cross section around a conducting solid and in an insulating or conducting medium. An external magnetic field is applied with an angle a with the axis of the pipe. The mathematical model of the considered physical problem can be defined in terms of coupled MHD equations in the pipe domain and the Laplace equations on the solid and external mediums. Due to the unbounded external domain and coupled form of the MHD equations, the FEM and BEM coupling approach is used which has many advantages in the view of discretization, computational time and stabilization. In the solution procedure, the fluid domain is discretized by the FEM elements, and the boundaries of the solid and the conducting mediums by the BEM elements. Proposed coupled numerical scheme is tested especially for the high values of the problem parameters and obtained stable solutions are displayed in terms of figures. (C) 2017 Elsevier Ltd. All rights reserved.