In the study of borehole instability, the majority of input parameters often rely on the average values that are treated as fixed values. However, in practical engineering scenarios, these input parameters are often accompanied by a high degree of uncertainty. To address this limitation, this paper establishes a borehole stability model considering the uncertainty of input parameters, adopts the Monte Carlo method to calculate the borehole stability reliability at different drilling fluid densities, evaluates the sensitivity of borehole instability to a single parameter, and studies the safe drilling fluid density window at different borehole stability reliability values under multi-parameter uncertainties. The results show that the uncertainty of rock cohesion has a great influence on the fracture pressure of the vertical and horizontal wells. The minimum horizontal stress has the greatest influence on the fracture pressure of the vertical and horizontal wells, followed by pore pressure. In the analysis of borehole stability, the accuracy of cohesion and minimum horizontal stress parameters should be improved. In scenarios involving multiple parameter uncertainties, while the overall trend of the analysis results remains consistent with the conventional borehole stability outcomes, there is a noteworthy narrowing of the safe drilling fluid density window. This suggests that relying on conventional borehole stability analysis methods for designing the safe drilling fluid density window can considerably increase the risks of borehole instability. Uncertainty assessment is crucial to determine the uncertainties associated with the minimum required mud pressure, thereby ensuring more informed decision-making during drilling operations. To meet practical application demands, structure and boundary condition uncertainties should be implemented for a more comprehensive assessment of borehole stability.