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A two-dimensional magnetohydrodynamical model describing the interaction of thin shock waves with turbulence is developed by adopting a multiscale perturbation analysis. The interaction is found to be governed by a two-dimensional inviscid Burgers’ equation that includes “perturbation terms.” Initially prescribed perturbation profiles are explored with numerical simulations to show how the shock front is modified by turbulence. Our numerical simulations show that magnetic field perturbations play a very important role in modifying the structure of perpendicular and parallel shocks. While turbulence can balance the nonlinear steepening of a shock wave at some regions, it can also help to create a larger jump in physical quantities such as the magnetic field at other regions. The plasma medium in these regions can therefore experience a higher compression, which will result in a downstream state that differs from the usual Rankine–Hugoniot state. [ABSTRACT FROM AUTHOR]