The performance of three advanced constitutive models has been evaluated based on element tests and on a comparative study on the simulation of vibratory pile driving tests in saturated sand. The inspected constitutive models are the Sanisand model and Hypoplasticity with Intergranular Strain (Hypo+IGS) as well as with Intergranular Strain Anisotropy (Hypo+ISA) extension. The performance of the constitutive models is first evaluated by the simulation of element tests used for the parameter calibration of the sand used in the model tests. The constitutive models are then applied for the simulation of a vibratory pile driving test. The pile penetration, the driving force, the pore water pressure development and the incremental displacement in the vicinity of the pile tip are compared to the measurements in the model tests. The strengths and weaknesses of the different constitutive models are assessed. Generally, the model predictions showed good agreement with the experimental results. Despite different constitutive formulations (hypoplastic vs. elasto-plastic), all three models were able to reproduce the main mechanisms of the driving process properly. It may be concluded that all three models allow a proper prediction of vibratory pile driving as long as a proper calibration of the material parameters is secured.