Abstract <p>This study theoretically and experimentally investigates the sloshing behavior that occurs when a circular cylindrical rigid tank is subjected to horizontal harmonic excitation and the excitation frequency is close to the natural frequency of the sloshing mode (1, 1). The fluid velocity potential and free-surface elevation are assumed in Galerkin’s expansion forms to solve the corresponding partial differential equations. Subsequently, the ordering assumption for each sloshing mode leads to the derivation of second-order ordinary differential equations for seven sloshing modes, including the two orthogonal and degenerate (1, 1) sloshing modes. Linear viscous damping terms are incorporated into the modal equations of motion to represent the viscous effects of the fluid. These equations form an autoparametric system in which only the (1, 1) mode, with a diametral nodal line perpendicular to the direction of tank motion, is directly excited by the horizontal translation of the tank and nonlinearly couples with the remaining sloshing modes. Frequency response curves are obtained from the resulting equations using van der Pol’s method and are compared with experimental results to demonstrate the high accuracy of the calculated responses. To investigate the influence of the excitation amplitude on bifurcation point transitions, the corresponding bifurcation sets are calculated, and the oscillation patterns of sloshing—planar motion, swirl motion with constant and modulated amplitudes, and chaotic swirl motion—are presented as occurrence boundaries. Therefore, reliable and convenient modal equations for nonlinear sloshing behavior are provided, enabling easy prediction of actual sloshing phenomena.</p>