In this study, the numerical solution of the magnetohydrodynamic (MHD) flow is considered in a circular pipe around a conducting solid and in an insulating or conducting medium. An external magnetic field is applied through axis of the pipe with an angle alpha with through the x-axis. 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. The coupled equations are transformed into decoupled inhomogeneous convection-diffusion type equations in order to apply stabilization in the finite element method solution procedure. Obtained stabled solutions for the high values of the problem parameters display the well-known characteristics of the MHD pipe flow.