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We present and compare three elastoplastic models currently used for deformation of metallic glasses, namely, a von Mises model, a modified von Mises model with hydrostatic stress effect included, and a Drucker-Prager model. The constitutive models are formulated in conjunction with the free volume theory for plastic deformation and are implemented numerically with finite element method. We show through a series of case studies that by considering explicitly the volume dilatation during plastic deformation, the Drucker-Prager model can produce the two salient features widely observed in experiments, namely, the strength differential effect and deviation of the shear band inclination angle under tension and compression, whereas the von Mises and modified von Mises models are unable to. We also explore shear band formation using the three constitutive models. Based on the study, we discuss the free volume theory and its possible limitations in the constitutive models for metallic glasses.