Nonlinear responses of the predominant two sloshing modes in a square tank have been investigated when the tank is subjected to horizontal, narrow-band random ground excitation. Galerkin’s method is applied to derive the modal equations of motion for nonlinear sloshing. Then the Monte Carlo simulation is used to calculate the mean square responses of these two modes. These to modes are nonlinearly coupled with each other, known as ‘autoparametric interaction’. The responses differ significantly from those of the corresponding linear model, depending on the characteristics of the narrow-band ground excitation such as the bandwidth, center frequency and the intensity. In addition, it is found that the direction of the excitation is a significant factor in predicting the mean square responses.