For the accurate prediction of the dynamic behaviour of geotechnical structures, such as dams, retaining walls and slopes, during seismic loading, the development of advanced numerical models is essential. They must include sophisticated constitutive models having the ability of accurately reproducing the complex mechanical behaviour of soils under cyclic shearing. Experimental data show that soil behaviour is influenced by state variables, such as the initial density, initial mean stress, initial static shear stress ratio (ISSSR) and the loading direction [1]. Preliminary numerical investigations indicate that for plane strain conditions shaking occurring perpendicular to the plane of the slope, so-called anti-plane loading, can lead to larger deformations of the slope compared to the in-plane loading case [2]. However, so far, these investigations are only restricted to numerical simulations with a hypoplasticity model. Moreover, the influence of ISSSR on the behaviour of the slope was not systematically investigated yet. To fill this gap, this contribution focusses on the influence of ISSSR and bi-directional loading conditions on the mechanical behaviour of the slopes. In order to reduce the complexity of the numerical model, we restrict our investigations to the case of infinite slopes (1D boundary-value problem), undrained conditions and a harmonic base excitation. For comparison purposes, the simulations are conducted using two advanced hypoplastic models. The influence of ISSSR is systematically investigated by considering different slope angles for both in-plane and anti-plane shaking. The simulation results show that for in-plane shaking, the largest deformation accumulation occurs at moderate ISSSR and not at the highest ISSSR, as one would initially expect. The opposite behaviour is observed during anti-plane loading.