During drilling operations, the wellbore pressure is subjected to fluctuations caused by some factors such as swab and surge pressure which can result in wellbore instability. In this research, a numerical model is built using the ABAQUS software to demonstrate the effect of swab and surge pressure on the wellbore’s growth of natural fracture and the time dependent pore pressure. A MATLAB program is then developed to determine the safe mud window by computation of the time dependent wellbore collapse pressure and fracture pressure. The results demonstrated that the fracture width as a function of time profiles increased with the swab and surge pressure. The biggest percentage increase of the fracture width after incorporation of swab and surge pressure was 70%. Interestingly, an increase of 69% of the fracture width was observed in the near wellbore region after application of swab and surge pressure. However, the fracture length, the loss circulation rate and the pore fluid pressure remained relatively unchanged after integration of swab and surge. The analysis of the time-dependent wellbore stability revealed that the mud window, which was initially constant, narrowed with the time after integration of swab and surge pressure. The collapse pressure without swab and surge pressure increased by 14% while the fracture pressure decreased by 14%. The numerical model was verified by evaluating the gap between ABAQUS numerical results and analytical solutions and good consensus was observed after comparisons. The model developed in this research can be useful for wellbore strengthening studies to determine the optimal Particle Size Dimension necessary to plug the natural fractures and mitigate the lost circulation.