Employing the multipole-type functions given by Faltinsen & Timokha (J. Fluid Mech., vol. 665, 2010, pp. 457–479), we derive a Trefftz-type representation of the velocity potential for the liquid sloshing problem in a two-dimensional circular tank. This representation defines a continuation of the velocity potential into the ‘air’ area confined by the ‘dry’ tank surface. Its usage facilitates an effective approximation of the natural sloshing modes for all tank fillings.