This thesis focuses on the study of spectral stability of planar shock waves in 2-dimensional magnetohydrodynamics. We begin with a numerical approach, computing the Lopatinski determinant and Evans function with the goal of determining if there are parameters for which viscous waves are unstable and the corresponding inviscid waves are stable. We also begin developing a method to obtain an explicit, analytical representation of the Evans function. We demonstrate the capabilities of this method with compressible Navier-Stokes and extend our results to 2-D MHD. Finally, using compressible Navier-Stokes again, we derive an energy estimate as a first step in improving the bound on possible roots of the Evans function.