<p>Soft structures composed of incompressible hyperelastic materials suffer from geometrical and material nonlinearities during deformation, which can lead to large deformations and large displacements, so it is required to maintain high continuity in the displacement field. However, it is difficult to ensure the high-order continuity requirement by using traditional finite element methods (FEM) which have the C° continuous elements. Nonlinear FEM represented by ANCF have been used to address issues in flexible multi-body systems. However, the ANCF method uses slope vectors as node coordinates, resulting in high degrees of freedom for each element and serious locking issues, which affect the computational efficiency and accuracy of this method. In this paper, a novel calculation method of large deformations and large overall motions for the Euler–Bernoulli beam is proposed based on the isogeometric analysis (IGA) method. The method combines the simplified neo-Hookean and Mooney-Rivlin models with a one-dimensional beam element. The middle section of the beam is modeled using the non-uniform rational B-spline (NURBS), and it is combined with Green’s strain tensor to derive elastic force and Jacobi matrix expressions in the fully Lagrangian formulations. This method accurately describes large deformations and large overall motions with fewer elements and control points, significantly improving computational efficiency. Compared to traditional methods and commercial software, computation time is reduced by over 77% while maintaining reliable accuracy. The research in this paper provides a theoretical basis for the dynamic analysis of flexible arms.</p>