Reliability is one of important index in the analysis and evaluation of mechanical structure. Aiming at the problems of various failure modes and low efficiency of reliability evaluation for complex mechanical structures, the reliability analysis method based on polynomial chaos expansions is applied to the reliability analysis of mechanical structures by combining Monte Carlo random sampling and polynomial chaos expansions. In addition, considering the correlation of parameters and various failure modes in the limit state function, the reliability evaluation method of mechanical structure considering failure correlation is given. Finally, a worm gear two-stage reducer is taken as an example to verify the proposed method according to analyzes the various limit state function of different failure form. The computational results show that the reliability evaluation method based on polynomial chaos expansions is efficient and accurate in mechanical structure reliability analysis. And when failure correlation is considered, it is also simple because of avoiding the complex transformation calculation problem.