<p>This work presents the application of variational principles to an inhomogeneous beam having orthotropic material properties. A planar beam with arbitrary transverse loading has been considered. Variational asymptotic method (VAM), a synergy between variational principles and asymptotic expansion, has been used. Application of VAM has simplified the analysis by assisting in providing the solution equations in an ordinary differential equation (ODE) format. Moreover, these equations are in functional form. ODEs are easier to solve and facilitate a closed-form analytical solution, whereas the functional form widens the scope of these equations by permitting solutions for a wider class of inhomogeneity models. For illustrations, four different inhomogeneity models are adopted from the literature, and a closed-form solution for each has been presented. The verification of the obtained results has been done by comparing them with some of the prominent literature results, as well as with finite element analysis (FEA) results obtained using Abaqus. Furthermore, it has been observed that the analytical solutions of this study also perform very well in situations involving isotropic material properties. There has been a considerable savings in computational cost between an FEA analysis and the analytical analysis. Based on this, the following are some of the key contributions from this work: (a) The given formulation successfully handles orthotropic as well as isotropic materials. Isotropy is handled by doing suitable reductions in the stiffness coefficients of the orthotropic material matrix. (b) In line with the mechanics, the ordered warping solutions result in Euler–Bernoulli-type deformation in the zeroth order, whereas the higher-order solutions result in transverse shear contribution.</p>