A tuned liquid damper (TLD), which consists of rigid tanks partially filled by liquid, is a type of passive control devicerelying upon liquid sloshing forces or moments to change the dynamical properties and to dissipate vibrationalenergy of a structure. An analytical non-linear model is proposed for a TLD using rectangular tanks filled with shallowliquid under pitching vibration, utilizing a shallow water wave theory. The model includes the linear damping of thesloshing liquid, which is an important parameter in the study of a TLD as it affects the efficiency of the TLD. Shakingtable experiments were conducted for verification; good agreement between the analytical simulations and the experi-mental results was observed in a small excitation amplitude range. The simulations of TLD-structure interaction by usingthe proposed model show that the TLD can efficiently suppress resonant pitching vibration of a structure. It is also foundthat the effectiveness of a TLD for suppressing the pitching vibration depends not only on the mass of liquid in the TLDbut also on the configuration of the liquid as well as upon the position where the TLD is located. If the configuration ofthe liquid, i.e. the liquid depth and the TLD tank size, is designed suitably, the TLD can have a large suppressing momentand can be very effective even with a small mass of liquid.