In this contribution, we refine the beam formulation presented in [1] to address the specific behavior of soft, hyperelastic materials. These materials are capable of sustaining large deformations while remaining elastic, making traditional linear stress-strain models inadequate under high strain. To overcome this limitation, we start with incompressible neo-Hookean materials and extend the analysis to a broader class of constitutive models, where the elastic energy density is expressed quadratically in terms of a selected strain measure. This leads to a linear relation between strain and its energetically conjugate stress. By embedding this generalized hyperelastic law into the Euler–Bernoulli beam framework of [1], we correct the inaccuracies arising from simplistic assumptions and highlight the significant role of lateral strain effects. Under uniaxial loading, lateral strains can markedly influence the displacement field and the distance from the beam axis—introducing evaluation errors comparable to those due to geometric nonlinearity. We provide both analytical and numerical validation of expressions for axial force and bending moment, considering scenarios with and without lateral strain effects. This extended model, integrated into the nonlinear beam algorithm of [1], captures the complex interplay between material properties, geometric nonlinearities, and transverse deformations. Our results emphasize the importance of accounting for both material nonlinearity and lateral strain effects to avoid substantial errors in stress prediction—an insight of practical relevance for the reliable design of soft structures. Acknowledgment: Financial support received from the Czech Ministry of Education, Youth and Sports (ERC CZ, project No. LL2310) is gratefully acknowledged. REFERENCES [1] M. Jirásek, E. La Malfa Ribolla and M. Horák. Efficient finite difference formulation of a geometrically nonlinear beam element. International Journal for Numerical Methods in Engineering (2021), 122:7013–7053.