The paper establishes a computationally inexpensive method to deal with the dynamic response of liquid storage tanks subjected to seismic excitation including dynamic soil-structure interaction. The tank is modelled as a thin shell, the stored liquid is described asan inviscid and incompressible fluid and the soil medium is modelled as an elastic continuum.The dynamic response of the tank-liquid-soil system is derived in the frequency domain usingdynamic substructuring and mode matching. The tank vibrations are first expressed in terms ofthe in-vacuo shell modes while the liquid motion is described as a superposition of linear po-tentials. The soil reaction to the plate of the tank is derived on the basis of a boundary integralformulation with the excitation field being the seismic free-field ground motion. Due to its highcomputational efficiency, the proposed method is suitable when a large number of simulations isrequired as is the case in seismic risk analysis. It overcomes the limitations of most mechanicalanalogues used nowadays, while at the same time maintains an accuracy comparable to that offinite element models within a fraction of the computation time of the latter.