A stray light analysis of the Cryogenic Limb Array Etalon Spectrometer (CLAES), which is to be flown on NASA's Upper Atmospheric Research Satellite (UARS), was performed utilizing the Arizona's Paraxial Analysis of Radiation Transfer/Paraxial Analysis of Diffracted Energy (APART/PADE) computer code. Developed by the Electro-optics Laboratory of the R&D division of Lockheed Missiles and Space Co., Inc., CLAES is a Gregorian-Mersene optical system in a z-configuration especially designed to minimize the amount of earth infrared radiation scattered to the detector. Diffraction phenomena are controlled by field and aperture stops, thus becoming a second order effect. A high level of stray light rejection is crucial for CLAES in order to detect the signatures of trace molecular species in the stratosphere. Nominally, the earth's limb will be imaged 0.20° off the edge of the detector array. The dominant source of scattered radiation in this system is produced by the laam and primary mirrors, therefore, the polishing, coating and cleaning of these surfaces is vital to the ultimate overall system performance. Contamination control has thus become an important issue for the CLAES project. In order to help evaluate the accuracy of the CLAES APART/PADE model and to validate diffraction and scattered light control, a stray radiation analysis of the CLAES Brassboard Telescope was undertaken. The resultant Point Source Transmittance (PST) predictions are compared to actual off-axis response measurements. BRDF measurements of the Brassboard mirrors were used as a means to obtain the optimal CLAES APART/PADE model. Both the analytical results of the CLAES instrument and the Brassboard are presented in this paper.