A liquid storage tank has a very extensive role in the petrochemical industry, and earthquake damage will cause very serious consequences. Considering the fluid-solid coupling, material nonlinearity and liquid level shaking dynamic behavior, three-dimensional calculation models of non-isolated and isolated liquid storage tanks are established, respectively. 12 earthquake waves are selected from Pacific Earthquake Engineering Research Center (PEER), and there are three earthquake waves of reverse (R), strike slip (SS), reverse oblique (RO) and normal (N) focal mechanisms, respectively. The influence of the focal mechanism on the dynamic responses of the liquid storage tank is investigated. The effectiveness control of sliding isolation on a near fault earthquake is discussed. The influence of the diameter of the limiting device on the shock absorption effect is analyzed. The results show that the order of influence of four types of focal mechanisms on liquid sloshing wave height is as follows: RO$mathrm{>$R$mathrm{>$SS$mathrm{>$N. For the wall displacement, liquid pressure and effective stress of the tank wall, the response under N-type focal mechanism earthquake is generally larger than that of the other three types, and the difference of wall displacement, liquid pressure and wall effective stress under RO, R and SS focal mechanism earthquakes is small. The results show that the dynamic responses of the liquid storage tank under different focal mechanism earthquakes is quite different. Sliding isolation can significantly reduce the dynamic responses of the liquid storage tank under strong near-fault earthquakes, and the diameter of the limiting device will affect the shock absorption effect of sliding isolation.