Peristaltic pumps are commonly used in medical applications like cardiopulmonary bypass and drug infusion due to their minimal contact with bio-fluids and precise flow control. However, these pumps generate inherent flow pulsations, which can cause backflow or strain on the fluid, potentially leading to issues like hemolysis in blood. This study investigated the mechanics of pulsation in the output mass flow rate of peristaltic pumps and explored strategies for reduction. Using an optimized tube geometry, 3D fluid–structure interaction simulations were conducted under realistic conditions. Tracking the pressure variations before and after each roller revealed a direct correlation with the transient drops in mass flow rate during roller disengagement. By adjusting geometric parameters, results indicated that selecting an optimal roller diameter could reduce pulsation by 20%. Variations in tube wall stiffness and curvature radius had minimal impact on mass flow rate. Notably, removing external support from the pump housing near the outlet reduces flow pulsation by up to 23% by enabling a smoother disengagement of the leading roller. Finally, this paper introduces a cost-effective volumetric approach to estimate mass flow rate trends during full tube occlusion, showing good agreement with the CFD model data.