This study is concerned with the reliability-based optimum design of a stiffened panel made of magnesium alloy subject to natural frequency. The panel is regarded as failure when the natural frequency is lower than an allowable limit. Since the lowest mode may be shifted due to variations of random variables, the panel failure is modeled as a series system consisting of several vibration modes. The mode reliability is evaluated by the first order reliability method (FORM), where the Young's modulus and panel dimensions have variations. In order to avoid the reliabiltiy overestimation, the tunneling algorithm modified to the FORM is utilized. The system reliability is approximated by Ditlevsen's upper bound. The total weight is minimized subject to the system reliability constraints in terms of the panel dimensions. Through numerical calculations, the reliability-based optimum design is demonstrated to be different from the deterministic optimum design. The results show the importance of considering variations of the random variables for the safety in designing a magnesium alloy structure.