This research proposes a reliability-based topology optimization (RBTO) using the finite element method. RBTO is a topology optimization based on probabilistic (or reliability) constraints. Young's modulus, thickness, and loading are considered as the uncertain variables and RBTO is applied to static and eigenvalue problems. The RBTO problems are formulated and a sensitivity analysis is performed. In order to compute probability constraints, two methods-RIA and PMA-are used. Several examples show the effectiveness of the proposed method by comparing the classical safety factor method.