We describe the purpose, theory, implementation and sample results of a wave optics propagation simulation developed to study multi-conjugate adaptive optics (MCAQ) for 4-10m class telescopes. This code was more specifically developed to assess the impact of diffraction effects and a variety of implementation error sources upon the performance of the Gemini-South MCAO system. These errors include: Hartmann sensing with extended and elongated laser guide stars, optical propagation effects through the optics and atmosphere, laser guide star (LGS) projection through the atmosphere, deformable mirror (DM) and wave front sensor (WFS) misregistration, and calibration for non-common path errors. The code may be run in either a wave optics or geometric propagation mode to allow the code to be anchored against linear analytical models and to explicitly evaluate the impact of diffraction effects. The code is written in MATLAB, and complete simulations of the Gemini-South MCAO design (including 3 deformable mirrors with 769 actuators, 5 LGS WFS with 1020 subapertures, 3 tip/tilt natural guide star (NGS) WFS, and 50 meter phase screens with 1/32nd meter resolution) are possible using a Pentium III but require 1 to 6 days. Sample results are presented for Gemini-South MCAO as well as simpler AO systems. Several possibilities for parallelizing the code for faster execution and the modeling of extremely large telescopes (ELT's) are discussed.