Purpose The paper aims to present a numerical modeling procedure for the analysis of liquid sloshing in a flexible tank subjected to an external excitation, with taking into account the effects of fluid–structure interaction (FSI). Design/methodology/approach A numerical model based on coupling a two-phase flow solver and an elastic solid solver is developed in OpenFOAM code. The Arbitrary Lagrangian–Eulerian formulation is adopted for the two-phase Navier–Stokes equations in a moving domain. The volume of fluid (VOF) method is applied for the air–liquid interface tracking. The finite volume method is used for the spatial discretization of both the fluid and the structure dynamics equations. The FSI coupling problem is solved by an explicit coupling scheme. The model is validated for linear and nonlinear sloshing cases. Then, it is used to analyze the effects of the liquid sloshing on the dynamic response of the tank and the effects of the tank flexibility on the liquid sloshing. Findings The obtained results show that the flexibility of the tank walls amplifies the amplitude of the sloshing and increases the fluctuation period of the air–liquid interface. Furthermore, it is found that the bending moment acting on the tank walls may be underestimated when rigid walls assumption is adopted as usually done in sloshing tank modeling. Also, tank walls flexibility causes a phase shift in the free surface dynamic response. Originality/value A review of previous studies on liquid sloshing in flexible tanks revealed that FSI effects have not been clearly and comprehensively analyzed for large-amplitude liquid sloshing. Many physical and numerical aspects of this problem still require clarifications and enhancements. The added value of the present work and its originality lie in the investigation of large-amplitude liquid sloshing in flexible tanks by using a staggered coupling approach. This approach is carried out by an original combination of a linear solid solver with a two phase fluid solver in OpenFOAM code. In addition, FSI effects on some response quantities, identified and analyzed herein, have not been found in the previous works.