Abstract: The effect of formation damage zone due to well drilling on partially penetrating wells is different from that on open-hole wells. In order to analyze the effect of damage zone on pressure response at the well bottom, this paper presents a 2D axial symmetry porous flow model for partially penetrating well. The model considers the actual formation damage zone around the wellbore and reservoir permeability anisotropy. The bottom-hole pressure response curves and pressure fields of partially penetrating wells are obtained by using the FEM method. The analysis of the pressure response curves and pressure fields shows that five flow regimes may appear in the pressure response process of partially penetrating wells. The early-time radial flow and the ellipsoidal flow are typical characteristics of partially penetrating wells. The effect of damage zone is studied. It shows that the skin factor S in traditional methods is not the mechanical skin factor S_d due to the formation damage. The dimensionless wellbore storage coefficient cannot combine with the mechanical skin factor. The wellbore pressure obtained from traditional methods is modified. The formula for total skin factor of partially penetrating wells is verified. Those conclusions provide theoretical guidance for the transient pressure data interpretation and productivity prediction of partially penetrating wells.