This paper presents a model to describe the behavior of sloshing in a general tank with a uniform fluid depth. An equivalent linearized mechanical model is developed for a tuned liquid damper (TLD) with arbitrary tank geometry. The finite element method is employed to determine the mode shapes of the sloshing fluid. In general, the mode shapes of arbitrary tanks will have response components in the x- and y-directions. The mode shapes enable the generalized properties of the sloshing fluid to be determined; these properties are subsequently used to establish equivalent mechanical properties. The nonlinear damping of slat-type damping screens is linearized, permitting it to be included in the model as amplitude-dependent viscous damping. The proposed model is in excellent agreement with existing linearized models for the special cases of rectangular and circular tanks. Sinusoidal shake table tests are conducted on tanks with chamfers placed in selected corners. In the literature, no experimental testing has focused on tanks of arbitrary shape with a constant fluid depth. The proposed model is in good agreement with the experimental results for the mode dominated by motion in the direction of excitation. However, the model is found to underestimate the response of the mode which is dominated by motion perpendicular to the excitation direction. The linearized mechanical model developed can serve as a useful preliminary TLD design tool.