Surge/swab pressure is a crucial parameter that provokes well-control problems such as fluid loss, fractured formations, fluid influx, and kick. Thus, a precise estimation of differential pressure is required to evade any unforeseen drilling difficulties. The existing predictive models are based on narrow-slot approximation methods and consider the effect of drilling string axial movement on downhole pressure surges. However, it ignores the impact on the boundaries of the annular fluid velocity zone by the tripping velocity. In this research, a simplified model is developed using the flow velocity profile generated in the annulus by the tripping operation and the concentric annular Couette fluid flow phenomena for power-law fluid. A comparative study is performed with the existing analytical models and the experimental data to validate the developed model. The obtained results are convincingly in good agreement with the analytical and experimental data. A parametric study is performed to identify the effect of various parameters on surge/swab pressure. It is found that the diameter ratio has a significant impact on pressure differential with the increase in the tripping velocity. The fluid behavior index exhibits a considerable effect, and fluid consistency index shows a minor effect on the surge pressure gradient. The simplified developed model requires less numerical analysis to determine the outcomes for varying industrial applications, especially petroleum drilling operations.