This study presents a new model for predicting the response of a two-dimensional tuned liquid damper (TLD) tank with a variable fluid depth. A simple finite element method is presented, which is used to calculate the sloshing mode shapes. From the mode shapes, the equivalent mechanical properties of the sloshing fluid are estimated. Three tanks (flat-bottom, triangular-bottom, and circular-bottom), which have closed-form expressions for their equivalent mechanical properties are used to evaluate the model. The proposed model is in agreement with the closed-form expressions. Subsequently, a parametric study is conducted on tanks with a chamfered-bottom, boxed-bottom, and ramped-bottom to assess how their properties change as the shape of the tank bottom is altered. The model provides TLD designers with greater flexibility when selecting a tank shape. Moreover, the model could be used to optimize the shape of a TLD tank to maximize its performance for a given liquid mass, allowing construction cost savings to be realized.