This study explores the use of a recent metaheuristic algorithm called a reptile search algorithm (RSA) to handle engineering design optimization problems. It is the first application of the RSA to engineering design problems in literature. The RSA optimizer is first applied to the design of a bolted rim, which is constrained optimization. The developed algorithm is then used to solve the optimization problem of a vehicle suspension arm, which aims to solve the weight reduction under natural frequency constraints. As function evaluations are achieved by finite element analysis, the Kriging surrogate model is integrated into the RSA algorithm. It is revealed that the optimum result gives a 13% weight reduction compared to the original structure. This study shows that RSA is an efficient metaheuristic as other metaheuristics such as the mayfly optimization algorithm, battle royale optimization algorithm, multi-level cross-entropy optimizer, and red fox optimization algorithm.