Shock waves in high-speed flows can drastically alter the nature of Reynolds stresses in a turbulent flow. We study the canonical interaction of homogeneous isotropic turbulence passing through a normal shock, where the shock wave generates significant anisotropy of Reynolds stresses. Existing Reynolds stress models are applied to this canonical problem to predict the amplification of the stream-wise and transverse normal Reynolds stresses across the shock wave. In particular, the efficacy of the different models for the rapid pressure-strain correlation mis evaluated by comparing the results with available DNS data. The model predictions are found to be grossly inaccurate, especially at high Mach numbers. We propose physics-based improvement to the Reynolds stress transport equation in the form of shock unsteadiness effect [Sinha et al., Physics of Fluids, 15, 2003] and enstrophy amplification for turbulent dissipation rate [Sinha. K, Journal of Fluid Mechanics, 707, 2012]. The resulting model is found to capture the essential physics of Reynolds stress amplification, and match DNS data for a range of Mach numbers. Numerical error encountered at shock waves are also analyzed and the model equations are cast in conservative form to obtain physically-consistent results with successive grid refinement. Finally, the proposed model for canonical shock-turbulence interaction is generalized to multi-dimensional flows with shock of arbitrary orientation.