In this work, 1 g model tests on vibratory pile driving in saturated sand are simulated, using different coupled element formulations in conjunction with a hypoplastic constitutive model. Owing to the high frequency of the vibrator in the model tests, the influence of the relative acceleration between the solid and water phases cannot be neglected a priori. The frequently applied u-p formulation assumes the relative acceleration to be zero; hence, two additional element formulations (the u-U and u-p-U approaches) are applied. A general investigation regarding the relative acceleration is first conducted using a semi-analytical approach, based on which the impact of the relative acceleration can be expressed by the wave frequency and hydraulic conductivity alone. Further, a threshold level of applicability of the u-p formulation is established. A comparison of the different element formulations used in the simulation of the vibratory driving model tests reveals that the relative acceleration has little impact, and the frequency threshold level obtained by the analytical solution holds. The simulations exhibit strong accordance with the experimental data in terms of pile penetration and pore pressure development. Different numerical aspects of the element formulations are discussed, including problems regarding volumetric locking and conditioning of the stiffness matrices.