The nematic liquid crystal variable retarder is a useful device for examining the polarization properties of optical components and material samples as well as for remote sensing applications. The response of the retarder to oblique ray angles is important in applications requiring a finite field of view such as imaging polarimetry. Mueller matrices that describe the response to incident angle are developed in two ways using an extended Jones matrix approach and through an alteration of a standard Stokes Mueller matrix for a retarder. Comparisons of the model results with lab measurements show good agreement, although with some differences due to varying assumptions in the models and nonideal aspects of the actual variable retarder. We provide analytical models that can be applied relatively easily to examine the effects of oblique angles in systems using liquid crystal variable retarders.