The design of a wooden impact limiter equipped to a transportation cask for radioactive materials was optimized. According to International Atomic Energy Agency Safety Standards, 9 m drop tests should be performed on the transportation cask to evaluate its structural integrity in a hypothetical accident condition. For impact resistance, the size of the impact limiter should be properly determined for the impact limiter to absorb the impact energy and reduce the impact force. Therefore, the design parameters of the impact limiter were optimized to obtain a feasible optimal design. The design feasibility criteria were investigated, and several objectives were defined to obtain various design solutions. Furthermore, a probabilistic approach was introduced considering the uncertainties included in an engineering system. The uncertainty of material properties was assumed to be a random variable, and the probabilistic feasibility, based on the stochastic approach, was evaluated using reliability. Monte Carlo simulation was used to calculate the reliability to ensure a proper safety margin under the influence of uncertainties. The proposed methodology can provide a useful approach for the preliminary design of the impact limiter prior to the detailed design stage.