SNAP is a proposed space-based experiment designed to study dark energy and alternate explanations of the acceleration of the universe's expansion by performing a series of complementary systematic-controlled astrophysical measurements. The principal mission activities are the construction of an accurate Type Ia supernova Hubble diagram (the supernova program) and conducting a wide-area weak gravitational lensing (WL) survey. WL measurements require highly constant point spread function (PSF) second moments (ellipticity), and the aim of this study is to expand on the 2005 Sholl, et al. preliminary work, specifically via use of the Ball Aerospace integrated modeling tool, EOSyM (End-to-end Optical System Model). This modeling environment combines thermal, structural and optical effects, including alignment errors, manufacturing residuals and diffraction, in an integrated model of the telescope. Thermo-mechanically induced motions and deformations of the mirrors are modeled as well as other disturbances, and corresponding ellipticity variations of the PSF are quantified for typical operational scenarios. In this study, the effects of seasonal variations in solar flux, transients introduced when pointing the body-fixed Ka-band antenna toward Earth, 90˚ roll maneuvers (planned every three months of operations) and structure dimensional changes associated with composites desorption are quantified and introduced into the optical system. Uncertainty in the telescope ellipticity distribution may be reduced by examination of foreground stars within the field of view. Reference is made to ongoing work on the use of foreground stars in quantifying the PSF.