The intent of this thesis is to simulate the effect of a background magnetic field on Rayleigh-Taylor (RT) instability morphology and evolution in support of a Discovery Science campaign at the National Ignition Facility. The RT instability is relevant in High Energy Density (HED) systems including supernova remnants such as the Crab Nebula and inertial fusion confinement (ICF). Magnetic fields affect RT evolution and can suppress small-scale fluid motion. Thus far no experimental work has quantified the effect of a B-field on RT evolution morphology. RT evolution under a B-field was examined in three-dimensional magnetohydrodynamic (MHD) simulations using the hydrocode ARES, developed by Lawrence Livermore National Laboratory. The parameter space of the experiment is explored to determine the parameters that yield a visible effect on RT evolution. The effect of resistive MHD and conductivity is examined to further establish the desired parameter space to observe the suppression of RT morphology.