The GUERAP III Monte Carlo simulation method traces the paths of statistical samples (rays) of energy flux as they interact with the surfaces of an optical system. To determine ray path interceptions, the surfaces are represented by analytical equations that define the surfaces and their boundaries. The result of each surface interaction is determined by probability distributions characterizing the optical properties of each surface. Property models include emission, absorption, reflection, and transmission (which includes refraction and diffraction). The semiempirical diffraction model assumes an angular probability density function of the distance of the ray from the edge of the aperture. The general surface equation and radiation model utilized permits analysis of complex visible and infrared systems with reflective and/or refractive elements. Although the program was written primarily for off-axis rejection analyses, it can also be used as a general on-axis ray tracing program for determination of such things as image quality and optical efficiency, including in a very natural way the effects of field of view, aberrations, obscurations, vignetting, diffraction, etc. In the off-axis mode the program is used for analySis of system sensitivity to scattering and diffraction, determination of the effectiveness of exterior and interior baffling mechanizations, and the identification of unwanted multipath ghost images.