Deterministic optimization may lead to unreliable design results if significant uncertainty exists. Including reliability constraints in reliability-based design (RBD) can solve such a problem. It is difficult to use current RBD methods to deal with time- and space-dependent reliability when responses vary randomly with respect to time and space. This study employs an envelope method for time- and space-dependent reliability for the optimal design. To achieve high accuracy, we propose an inverse envelope method that converts a time- and space-dependent limit-state function into a time- and space-independent counterpart and then use the second-order saddlepoint approximation to compute the probability of failure. The strategy is to find an equivalent most probable point for a given permitted probability of failure for each reliability constraint. To achieve high efficiency, we use a sequential optimization process to decouple the double-loop structure of RBD. The overall optimization is performed with a sequence of cycles consisting of deterministic optimization and reliability analysis. The constraints of the deterministic optimization are formulated using the equivalent most probable points. The accuracy and efficiency are demonstrated with four examples, including one mathematical problem and three engineering problems.