A stray light analysis of the Apache Point Observatory 3.5 meter telescope system was done to understand the performance for a variety of imaging modes. The telescope system consists of the 3.5-m telescope, its enclosure, and its associated imaging cameras. The purpose of the study was to assess the stray light performance of this system, identify where modification(s) would improve the system off-axis rejection characteristics, and assess the effectiveness of those modifications. A detailed telescope system geometry model was created, and scatter models were created for telescope and enclosure components. The computer model we created duplicated the pinhole stray light images taken with the telescope, thereby verifying the model. The Point Source Transmittance (PST), a commonly used metric for assessing stray light was used to evaluate the stray light performance of the system for a number of off-axis angles and to suggest modifications to enhance the system. The baseline PST of the existing system shows virtually no falloff with off-axis angle in the plane of the observatory slit. This is the result of (1) the focal plane having a large, unobstructed view of the Nasmyth mirror and cell, primary mirror cell, and baffles mounted on the Nasmyth cell, (2) relatively unobstructed illumination of telescope over a large range of angles in the plane of the slit, and (3) secondary and Nasmyth baffles that are not enclosed. These attributes create a series of first-level scatter paths that directly illuminate the focal plane. Our approach to stray light reduction was to address the light paths revealed by the various PST calculations. Our calculations have shown that significant gains can be realized with simple modifications to the telescope system.