Following previous experimental evidence of growth and arrest of Richtmyer-Meshkov instabilities in copper, we have used the CTH shock physics code to study and calibrate the effects of material strength at high strain rates. Highly resolved one and two-dimensional simulations were performed using the Johnson-Cook (JC), Mechanical Threshold Stress (MTS), and Preston-Tonks-Wallace (PTW) strength models. The one-dimensional simulations utilized a prescribed homogeneous deformation strain path covering strain rates observed in previous hydrodynamic instability experiments. Spall was modeled using a nominal threshold pressure model (PFRAC) and we use the Mie-Gruneisen equation of state to estimate the volumetric response of the experiments. Our results show good qualitative and quantitative agreement between numerical estimates and prior experiments in the strain rate regimes of interest.