Simulation of Gaussian laser beam propagation has many practical applications in teaching optics behavior and in laser design engineering. For the case of laser resonator cavity studies, most current techniques use the widely taught self-consistency round trip method to analyze the beam radius envelope through the cavity. We present a simpler method for simulating a confined Gaussian beam by modeling the real components of a complex ray. The procedure relies heavily on the classic multi-lens ABCD formulations for ray tracing optical cavities developed by Kogelnik, though it avoids the use of the q-parameter and its ABCD transfer law traditionally carried within the matrix optics transfer computations. Arnaud’s pioneering complex ray formulation and the Delano y-ybar ray theory provide the essential framework. The result is an easy computer simulation technique, which only requires a single calculation of the one-way complete traverse optical matrix. We present multiple detailed examples of our procedure for representative laser resonator beam simulations. The complex ray method significantly improved the efficiency of Gaussian beam ray tracing in cavities compared to the conventional q-parameter method. The optical elements considered only include end mirrors and intracavity thin lenses.