The basilar membrane (BM) and perilymph motion in the cochlea due to rocking stapes motion (RSM) and piston-like stapes motion (PSM) is modeled by numerical simulations. The full Navier-Stokes equations are solved in a two-dimensional box geometry. The BM motion is modeled by independent oscillators using an immersed boundary technique. The traveling waves generated by both stimulation modes are studied. A comparison of the peak amplitudes of the BM motion is presented and their dependence on the frequency and on the model geometry (stapes position and cochlear channel height) is investigated. It is found that the peak amplitudes for the RSM are lower and decrease as frequency decreases whereas those for the PSM increase as frequency decreases. This scaling behavior can be explained by the different mechanisms that excite the membrane oscillation. Stimulation with both modes at the same time leads to either a slight increase or a slight decrease of the peak amplitudes compared to the pure PSM, depending on the phase shift between the two modes. While the BM motion is dominated by the PSM mode under normal conditions, the RSM may lead to hearing if no PSM is present or possible, e.g., due to round window atresia.