Mixed wave systems are systems governed by wave equations that in the semiclassical limit have coexisting chaotic and regular trajectories. The goal of this study is to calculate the statistics of the response of mixed systems to external excitation. The ray tracing method is used to explore the property of simple two-dimensional wave system shapes: the “Four Arcs” and the “Peanut” billiard. The ray trajectories for these two mixed systems are plotted in real space and in phase space. The goal is to apply the generalized Random Coupling Model (RCM) to study the response of these two mixed systems in the form of their impedance matrices. To obtain information needed for the generalized RCM, the Method of Moments (MOM) is implemented to numerically calculate the eigenfrequencies and eigenmodes of the 2D cavities under consideration. As a preliminary study statistics of a lossless and a lossy impedance for a two-port 2D rectangular cavity are calculated.