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In this paper, by defining a novel analytical derivation method for a composite beam, using the suitable assumptions, the stiffness coefficients and torsional rigidity (shear modulus) for single-cell and multi-cell thin walled layer wise composite sections of a beam are calculated. The results are presented in the form of Maple and FORTRAN codes in order to calculate these parameters in a timely manner. These parameters are used for the preliminary structural analysis of the beam. The nonlinear Euler Bernoulli beam assumptions are used to derive the stress-strain and strain-curvature relations. Next, by using the potential energy and elastic curvature relation for elastic beams, the stiffness parameter is calculated. Then, the equivalent torsional rigidity is introduced for single and multi-cell thin walled layer wise composite sections, using the stiffness parameter. To verify the validity of the computations, the results are compared with the numerical results obtained from a finite element analysis. The results show that applying this method for the calculation of the torsional rigidity of single and multi-cell thin-walled composite sections is a viable method and is very useful in obtaining a suitable, initial analytical approximation in the preliminary design of engineering structures, particularly in that of composite structures utilized in aerial industries.