While suction cups are widely used in Robotics, the literature is underdeveloped when it comes to the modelling and simulation of the suction phenomenon. In this paper, we present a novel physically-based approach to simulate the behavior of active suction cups. Our model relies on a novel formulation which assumes the pressure exerted on a suction cup during active control is based on constraint resolution. Our algorithmic implementation uses a classification process to handle the contacts during the suction phenomenon of the suction cup on a surface. Then, we formulate a convenient way for coupling the pressure constraint with the multiple contact constraints. We propose an evaluation of our approach through a comparison with real data, showing the ability of our model to reproduce the behavior of suction cups. Our approach paves the way for improving the design as well as the control of robotic actuators based on suction cups such as vaccum grippers.