Abstract The first order reliability method (FORM) efficiently performs first order structural reliability analysis, but with limited accuracy. On the other hand, the traditional second order reliability method (SORM) was established to improve the results of FORM, but with a supplementary computational process. Proposed herein, is a new SORM, based on differential geometry making SORM more efficient without hindering accuracy. It can be used to perform the second order structural reliability analysis in engineering. A case in the geotechnical engineering field obtained from literature was solved aiming to demonstrate the ability of the analytical procedure via differential geometry. The advantages of the newly proposed approach whereby the reliability method by differential geometry (SORM DG) over the traditional SORM are discussed. The results show that the SORM DG optimizes the outcomes from FORM and achieves the accuracy of the traditional SORM, more efficiently.