Recently, an explicit analytical solution for general laminated composite beams with coupled stretching–bending and transverse shear deformation has been developed using the matrix exponential method [1]. Further extension was also made for stretching–bending–torsional coupling without warping deformation [2]. Several analytical results were derived for typical beam configurations under different load cases. However, when the torsional warping effect is ignored, the torsional stiffness is overestimated and the predicted rotation angles become inaccurate for beams with non-circular cross-sections. This limitation can reduce the reliability of analytical solutions in practical design and analysis. In this study, the classical displacement field assumed in Timoshenko beam theory is further extended to include torsional deformation with an additional warping parameter, resulting in seven degrees of freedom: three axial displacements, two bending angles, one torsional angle, and one warping parameter. The governing equations for the fully coupled stretching–bending–torsional problem with warping deformation can still be expressed in a unified matrix form similar to the case without warping, but with expanded matrix size and modified entries. Retaining the matrix exponential framework is important for deriving analytical expressions, although the inclusion of warping introduces potential divergence and singularity issues that require specialized numerical treatment. To demonstrate the effectiveness of the proposed formulation, several numerical examples are presented. The effects of composite properties, cross-sectional shape and loading type are investigated. Comparisons with results obtained from the commercial finite element software ANSYS show good agreement, validating the accuracy of the newly-derived analytical solutions. The extended model provides a more accurate and reliable tool for analyzing composite beams with significant torsional warping effects. REFERENCES [1] W.Y. Huang, C. Hwu and C.W. Hsu, 2024, “Explicit analytical solutions for arbitrarily laminated composite beams with coupled stretching-bending and transverse shear deformation,” European Journal of Mechanics - A/Solids, Vol. 103, 105147. [2] Y.S. Wei and C. Hwu, 2024, “Coupled Stretching-Bending-Torsional Analysis of Laminated Composite Beams,” Abstract book of 17th International Conference on Advanced Computational Engineering and Experimenting (ACEX2024), Barcelona.