Splines are a special type of mathematical function that allow easy control of the shape of the object to be modelled. In this paper, we present a method to compute the radar cross section of spline-modelled cavities. The advantage of spline-modelled cavities is that they can model with very good precision almost any real cavity. The method to compute the radar cross section of the cavities is known as the GO+PO method, and consists of modelling the incident wave as a set of parallel rays that come inside the cavity, bounce against its walls, and finally exit from the aperture. We have developed a method to propagate GO rays inside the cavity without losing precision in the many bounces each ray suffers, based on techniques similar to those used in computer graphics to create real images. Different approximations have been studied to model the fields in the aperture when the rays reach it after bouncing inside the cavity. With the chosen model and the theorem of equivalent magnetic currents, we can compute the fields reradiated by the aperture and then the radar cross section of the cavity.