This paper presents a novel method for tracking multiple extended objects. The shape of a single extended object is modeled with a recently developed approach called Random Hypersurface Model (RHM) that assumes a varying number of measurement sources to lie on scaled versions of the shape boundaries. This approach is extended by introducing a so-called Mixture Random Hypersurface Model (Mixture RHM), which allows for modeling multiple extended targets. Based on this model, a Gaussian-assumed Bayesian tracking method that provides the means to track and estimate shapes of multiple extended targets is derived. Simulations demonstrate the performance of the new approach.