Excessive tripping speed in an uncased borehole increases the risk of having formation damage or influx of formation fluid (kick). However, if the tripping is performed at lower speeds, the operation requires more rig time. Hence, increased trip speed cuts expensive rig time. These opposing goals require thorough planning and optimization of the tripping operation to avoid operational problems and reduce financial expenditures. To maximize the tripping speed, accurate prediction of the pressure change occurring due to the axial pipe movement (surge or swab pressure) is necessary. The pressure change is influenced by the hole and string diameters, eccentricity, fluid properties and trip speed. The tripping speed is one of the operational parameters, which are regularly adjusted at the rig site. Analytical solutions exist only for special scenarios. The semianalytical models for calculation of the steady-state pressure change cannot provide accurate predictions. They are mostly based on disputable assumptions which make the model to underestimate the pressure change. Most of the existing models are based on the parallel-plate approximation of the annular geometry. In another approach, the parameter, which reflects the amount of fluid which is dragged the direction of the string, assumed to be constant or calculated independent of the fluid viscosity. In this paper, accurate solutions were obtained from direct numerical simulation of flow in a cylindrical annulus with axial movement of the inner cylinder. The numerical algorithm is based on finite volume method and incorporates laminar flows of Newtonian, Power Law, Bingham Plastic and Herschel-Bulkley fluids. The method predicts the pressure change occurring in concentric and eccentric annuli with and without rotation of the inner cylinder. The goals of this work are to: i) study the influence of the eccentricity, fluid properties and tripping speed on the pressure change; and ii) evaluate the accuracy of the simplified approaches by comparing experimental data and numerical solutions, and determine their validity ranges. This paper presents a new method for finding trip-caused pressure change in the wellbore through systematic analysis of the numerical solutions. Parametric study was performed to examine the effects of different influential parameters on the pressure change. In addition, the results obtained from the numerical method are compared with the simplified solutions and the discrepancies are analyzed to show the improved accuracy of the new method.