Many cities around the world have adopted Bike Sharing Systems to offer an alternative to personal vehicles and classic public transport. These systems present many challenges. One of those challenges is the availability of both bikes and docking stations, which has a direct influence on the user satisfaction level. Operator of such a system uses a vehicle fleet dedicated to the repositioning of bikes from full stations to empty ones. This operation, often performed during the night when the demand is negligible, is referred in the literature as static rebalancing. The problem consists in determining the number of bikes to pickup and/or deliver at each station, in order to increase, or even optimize, the availabilities of both bikes and docking stations. The models proposed in the literature are generally linear programming models, which may be hard to establish without proper knowledge of mathematical programming techniques. In this paper, we propose a method for helping the building of these mathematical models through the use of UML graphical class diagrams which describe the structure and properties of a bike sharing system. Transformation rules are defined to extract some constraints of the problem from the system class diagram. The mathematical model is then completed by adding additional constraints as well as the objective function that cannot be expressed in UML language. We will use the case of the Parisian bike sharing system (Vélib’) to illustrate the method.