This thesis is concerned with the effects of earthquakes on partially-filled water tanks. The analysis is applicable to rectangular water tanks, which have received little attention to date. The analysis is relatively involved and includes the derivation of the equations of motion for the vibration of the whole of tank by means of substructure synthesis, a stochastic analysis relating the random ground motion caused by earthquakes to the random vibration of the tank, a stochastic characterization of the fluid pressure and computation of the probability of failure of the tank.