In order to estimate the mechanical components′ response reliability under interference of dynamic correlative stress-strength, the Copula function and random process theory were introduced to establish dynamic reliability model. Due to the complexity of random integral, the random process degenerates into random variable, and then the reliability at a fixed time was calculated based on the discretization thought. Furthermore, the function fitting optimization method was adopted to make the reliability value continuous. At the same time, according to model complexity and fitting residual, the optimal reliability function fitting method was selected. Finally, the typical verified example indicates the effectiveness and feasibility of this method.