Abstract: In this paper, the first four natural frequencies of the sloshing liquid in a rectangular tanker are initially measured using the vertical parametric excitation method. Subsequently, Faraday waves corresponding to the first four parametric sloshing modes are individually excited and recorded. The FFT (Fast Fourier Transform) filtering decomposition method is used to decompose the Faraday waves, and the multi-mode theory is applied to qualitatively analyze the mode composition and coupling mechanisms of the Faraday waves. The research reveals that Faraday waves can be decomposed into various mode motions, including the principal mode, rigid mode, double-frequency mode, triple-frequency mode, and so on. Among these, the principal mode is dominant and corresponds to a principal parametric resonance, in which the response frequency is half the excitation frequency. Other mode motions are excited by the principal mode motion and manifest as forced vibrations, with response frequencies equal to the excitation frequencies. The rigid mode motion shifts the liquid surface wave height response curve upward, resulting in wave crests with greater amplitude than the troughs. The odd-order Faraday waves no longer exhibit anti-symmetry in the steady state, whereas the even-order Faraday waves retain symmetry, indicating that the participating mode motions are exclusively even modes.