In this article, a two-step based sampling method is developed to solve the problem of maximizing the power transmission capacity in a system of V-belt driving with polymorphic uncertainties. The problem is first formulated as an optimization model, where there are a non-linear objective function and some linear or non-linear constraints associated with some parameters which are of uncertain nature. These uncertain parameters are interval parameters, random interval parameters, fuzzy parameters, or fuzzy interval parameters. To find a robust solution of the problem, the model of polymorphic uncertainty is converted into a non-linear interval programming problem; then, for a given satisfaction level, an interval solution for the original model is found by the developed two-step based sampling method. The proposed method is applied into a real-world design problem of V-belt driving, and numerical results indicate that both the model and the developed algorithm are useful to solve the maximization problem of the capacity in the system of V-belt driving.