In order to overcome the challenge of quantifying the influence of environmental conditions and the coexistence of multiple failure modes involved in mechanism reliability modelling under different environments. In this paper, we propose a method for the analysis of mechanism reliability that takes into account the influence of environmental factors and failure modes’ correlation, quantifies the influence of environmental factors as the random distribution and degradation path of parameters, and derives the Copula description of failure mode correlation from the historical data of environmental experiments. On the basis of the discrete mechanism dynamics model, the output parameters of the characteristic points are calculated, and the failure rate of each failure mode is calculated based on the failure criterion and the performance margin theory. Additionally, the dynamic change pattern of the mechanism reliability is compared with the Kaplan-Meier estimation of the corresponding environmental test history data to assess the validity of the calculation results. The reliability modelling problem of a motion mechanism of an automatic rifle automaton in a high and low temperature environment is applied to the method, and the reliability calculation results are close to those of Kaplan-Meier estimation of the test history data, and all are within the upper and lower bounds given by the reliability boundary theory, demonstrating the method's validity.