This study proposes a meshless interpolation method based on Interpolating Modified Moving Least Squares (IMMLS) to accurately simulate the large deformation behavior of hyperelastic materials. In numerical analysis, IMMLS is an advanced meshless interpolation technique based on the Element-Free Galerkin (EFG) method. Hyperelastic materials exhibit complex nonlinear constitutive relationships, making them a distinct class of elastic solids. These materials are typically analyzed within the framework of finite deformation theory due to their ability to undergo large strains. Therefore, a thorough understanding of their nonlinear behavior is essential for developing accurate and efficient numerical models. While traditional mesh-based approaches often struggle with large deformation problems, meshless techniques have demonstrated superior flexibility and the ability to overcome these limitations. To evaluate the effectiveness of the proposed method, the Neo-Hookean model was applied to assess the performance of the algorithm in large deformation problems. Material properties used in this study were obtained from existing literature to ensure accuracy. The simulation results were compared against those obtained using the Finite Element Method (FEM) as well as reference data from previous studies. Furthermore, the numerical algorithm and computational program were validated by benchmarking the results against reference solutions generated in MATLAB. Finally, the discussion is extended to explore potential applications of IMMLS, highlighting its relevance in broader engineering contexts. The findings of this study serve as a benchmark for future in-depth research in this domain.