Infrared observations of Tycho’s supernova remnant suggest that it is evolving into a strong ambient density gradient with a difference in density from one side to the other of a factor of 20. Yet the remnant appears remarkably spherical. Such a large density contrast might be expected to cause a change in the morphology and overall shape of the remnant as well as altering the location of the explosion with respect to the geometric center of the remnant. We use three-dimensional hydrodynamical simulations to explore the effects of an external density gradient on the shape and morphology of supernova remnants. These models demonstrate that even large density contrasts as observed in Tycho do not significantly alter the shape of the remnant. Aside from a brightness variation due to the differences in density around the perimeter of the remnant, there is very little effect on the observed morphology unless the density gradient becomes extreme (the length scale of the density variation is much less than the remnant radius).