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Understanding stress variations in pulsating flows due to periodic pressure gradients is fundamentally significant for the design and optimization of various medical apparatuses and for understanding biological phenomena. Oscillating flows have been dealt analytically and experimentally in great detail in the past. In this paper, a three-dimensional lattice boltzmann model is used to simulate the pulsating flows in a rectangular duct due to low, moderate, and high periodic pressure gradients. Asymptotic forms for velocity (valid for high frequencies) valid in different regions of the channel have been matched with the analytical results. The evolution of annular effects in the flow along with the Stokesian layer characteristics have been followed. Stress analysis at different points of the wall of the duct has been carried out to show regions of high stress and stress rates.