A modified pseudo-dynamic method is introduced in the paper at first, then geometric model of seismic stability on the waterfront rock slope considering the non-linear twin shear criterion is established. Finally the influence factors on the stability of rock slope are analyzed. The conclusions are drawn that the stability of rock slope decreases as the external loading $$q$$ q , rock unit weight $$\gamma$$ γ , horizontal seismic acceleration coefficient $$k_{h}$$ k h and vertical seismic acceleration coefficient $$k_{v}$$ k v increases, and it increases as uniaxial compressive strength $$\sigma_{c}$$ σ c , the water depth $$h_{1}$$ h 1 and parameters of rock mass properties $$m_{i}$$ m i and $$GSI$$ GSI of rocks increases. These conclusions can provide great instruction significance for the future engineering design.