Purpose This paper aims to present a new numerical model for geometric nonlinear analysis of thin-shell structures based on a combined finite-discrete element method (FDEM). Design/methodology/approach The model uses rotation-free, three-node triangular finite elements with exact formulation for large rotations, large displacements in conjunction with small strains. Findings The presented numerical results related to behaviour of arbitrary shaped thin shell structures under large rotations and large displacement are in a good agreement with reference solutions. Originality/value This paper presents new computationally efficient numerical model for geometric nonlinear analysis and prediction of the behaviour of thin-shell structures based on combined FDEM. The model is implemented into the open source FDEM package “Yfdem”, and is tested on simple benchmark problems.