High-speed flows over the surface of hypersonic airfoil subjected to several types of applied magnetic field distributions are numerically simulated. The governing equations are composed of the Euler equation modified to include the effect of magnetic field. In the current applications, the low magnetic Reynolds number approximation is utilized and the Hall effect and ion slip have been neglected. A fourth-order modified Runge-Kutta scheme augmented with the Davis-Yee symmetric Total Variation Diminishing model in post-processing stage is used to solve the magnetogasdynamics equations. The flow simulations are compared to the existing solutions. A good agreement between the present analysis and the available normal shock data is demonstrated. It has been found that the location and distribution of the imposed magnetic field have dominant effects on the flow parameters and the shock standoff distance.