Surge and swab pressures have been known as one of the most important factors for formation fracture, lost circulation and well control problems. Previous surge/swab pressures models are mostly based on Bingham plastic (BP) or Power law (PL) fluids, which cannot adequately describe the flow behavior of drilling fluid. This paper presents a new model for computing surge/swab pressures of Herschel-Buckley (HB) fluids in horizontal/directional wells which involves the effect of eccentric annuli. A axial laminar flow model in eccentric annulus is developed using narrow slot flow model with the H-B rheological model. The drilling fluid velocity model caused by the moving drillstring is developed, through which the flow rate can be calculated. Based on the equal flow rate from the flow model and the drilling fluid velocity model, the pressure gradient equation is obtained. The numerical solution of the pressure gradient is calculated utilizing adaptive Simpson integral method which is of high accuracy. Lastly, a case study is conducted. The model proposed in the current study is meaningful for safety drilling.