In the stability analysis and evaluation of slope engineering, its function usually presents highly nonlinear implicit characteristics, which makes it impossible to directly solve its reliability. Therefore, a combination has been proposed of Pade rational approximation in numerical analysis with the response surface method in reliability analysis, thus fitting the response surface function by using the Pade approximation rational polynomial. By adopting the Latin hypercube test, samples can be constructed, with the sample data substituted into the simplified Bishop algorithm, thus obtaining the value of slope function function, followed by the solution of the undetermined coefficients of proxy model, so as to realize the explicit expression of implicit function function. Based on the Matlab programming language, the JC method reliability index calculation program is compiled, thus establishing a new slope stability reliability analysis method (PRSM) based on the Pade approximation rational polynomial as well. The feasibility, efficiency and accuracy of the proposed method can be verified by two classic slope calculation examples. Finally, with the proposed method applied to an actual slope project, the calculation results show that the slope project is characterized with a low instability possibility, which is consistent with the actual monitoring results.