This paper describes a mathematical model and its utilization algorithm for calculating the accurate target position on the ellipsoidal earth surface which corresponds to a range-azimuth coordinates of unprocessed synthetic aperture radar (SAR) images. A geometrical model which is a set of coordinate transformations is described. The side-looking directional angle (off-nadir angle) is determined in an iterative fashion by using the model and the accurate slant range which is calculated from the range sampling timing of the instrument. The algorithm can be applied not only for the geolocation of SAR images but also for the high quality SAR image generation by calculating accurate Doppler parameters.