In this paper, the tristable stochastic resonance (SR) phenomenon induced by $\alpha$-stable noise is analysed. The mechanism for realizing resonance is explored based on research concerning the potential function and resonant output of a system. The rules for resonance system parameters $q$, $p$, skewness parameter $r$ and intensity amplification factor $mathcal{Q}$ of $\alpha$-stable noise to act on the resonant output are explored under different values of stability index $\alpha$ and asymmetric skewness $\beta$ of $\alpha$-stable noise. The results will contribute to a reasonable selection of parameter-induced tristable SR system parameters under $\alpha$-stable noise, and lay the foundation for a practical engineering application of weak signal detection based on the SR.