AbstractA finite element solution of the Navier‐Stokes equations for steady flow under the magnetic effect through a double‐branched two‐dimensional section of a three‐dimensional model of the canine aorta is discussed. The numerical scheme involves transforming the physical co‐ordinates to a curvilinear boundary‐fitted co‐ordinate system. The shear stress at the wall is calculated for a Reynolds number of 1000 with the branch‐to‐main aortic flow rate ratio as a parameter. The results are compared with earlier works involving experimental data and found to be in reasonable qualitative agreement. The steady flow, shear stress and branch flow under the effect of a magnetic field have been discussed in detail.