We present an initial evaluation of the role of the Richtmyer-Meshkov (RM) instability in supernova remnant (SNR) formation. Although the Rayleigh-Taylor (RT) instability is most often considered in the canonical picture of SNR formation, the theoretical penetration depths for RM instability suggest that it could play a significant role in the early stages of SNR formation. We have used the code PROMETHEUS to perform a sequence of two-dimensional hydrodynamic simulations in order to test this possibility. Here we discuss a case in which we impose a large perturbation in the expanding ejecta behind the reverse shock. The interaction of the reverse shock with the perturbation produces significant early RM growth, with spikes penetrating from the contact surface to near the forward shock. Then the RM instability weakens, RT growth eventually dominates, and the perturbation of the forward shock diminishes. We conclude that RM instability growth due to the type of perturbation we have studied might contribute to, but alone cannot account for, the observed radio and X-ray structures that extend to the forward shock in such SNRs as supernova 1006.