The Richtmyer-Meshkov (RM) instability of a flat density interface that is induced by a perturbed shock is simulated in this study. A rigid circular cylinder perturbs a planar shock wave that interacts with a flat density interface, initiating the RM instability. The compressible Euler equations that govern the dynamics of the inviscid shock wave are numerically solved by a second-order multidimensional upwind embedded boundary method wherein the cylinder geometry is implicitly represented by a level-set function. A block-based adaptive mesh is employed to refine the local complex areas and capture wave patterns and interfaces effectively. Three different distances η (the ratio of distance L from cylinder to interface over cylinder diameter D) are considered. The results show the interaction of the perturbed shock and the flat interface leads to the formation of overall “Λ”−shaped structures that characterize the interface perturbation. The growth of the perturbation width and depth is affected by distance L, and the width of the shock perturbation is determined by diameter D. Furthermore, the computational shape of incident perturbed shock and geometrical sizes of distorted interface are compared and analyzed with experimental results quantitatively.