Abstract. I will discuss a class of two-dimensional N = (2, 2) Gauged Linear Sigma Models (GLSM) called squashed toric sigma models. These models are deformations of toric GLSMs obtained by gauging the favor symmetries and introducing a set of corresponding compensator super fields. I will then talk about the elliptic genus of these models, using localization technique, in the case when the unsquashed vacuum manifolds obey the Calabi-Yau condition. I will also discuss the modular and elliptic properties of the elliptic genera of these models.