Abstract <p>Geometric nonlinear problems are common in engineering, and it is very difficult to obtain an analytical solution. Furthermore, mesh-based numerical methods suffer from high computational complexity, low efficiency and poor accuracy in solving the geometric nonlinear problems due to mesh constraints. To address this issue, this paper presents a nonlinear Hermite interpolation meshless method (HIMM) for large deformation analysis of elastomers. This method utilizes a set of discrete nodes to represent the problem domain, avoiding mesh generation and reconstruction. Firstly, the governing equations of the geometric nonlinear problems are obtained based on the virtual displacement principle and full Lagrangian formulation. Secondly, the approximation function of the displacement field is derived using the Hermite approximation method and moving least squares method. Then, the meshless formulation is obtained, and the HIMM model for the geometric nonlinear problems is established. Finally, the influence of the scale factor, load step and node density on the accuracy of the HIMM model is analyzed, and the effectiveness of the HIMM for solving geometric nonlinear problems is verified through several examples. The numerical results show that the computational accuracy of the HIMM is 3 to 6 times higher than that of the existing element-free Galerkin method (EFGM). In addition, the HIMM reduces the computation time by approximately 50% compared to the EFGM. This work provides an effective numerical tool for geometric nonlinear problems, and also provides a reference for applying meshless methods in the engineering field.</p>