The present report proposes an evaluation function of openability so as to evaluate opening ease of aluminum beverage bottles and to specify the rigorous dimension of cap diameter that is best suited for consumers' satisfaction. The evaluation function is defined as the ratio between the maximum torques that consumers can apply and the required torque for opening. In addition, the cap diameter is the only design variable, and the thumb length, which associates with the maximum gripping force, is selected as the state variable in order to take individual differences into consideration. Moreover, the function is formulated considering the uncertainty of opening actions of consumers. The function is composed by using the data obtained from the measurement of the maximum gripping force, the thumb length, and the opening actions, and then the function is optimized. The result of optimization shows that the optimum opening diameter is obtained at 30.6 mm. The thumb length associates with the maximum gripping force, and also affects the optimum opening diameter. The optimum opening diameter changes from 28 to 35 mm with the increase of the thumb length.