Assessing the internal strain fields locally within a composite is a challenging endeavor. In the specific case of randomly oriented fiber composites, approaches have been devised for analytical solutions using Eshelby’s method (which requires solving elliptic integrals in discrete regions of interest) and the Mori–Tanaka method (which combines Eshelby’s solution with homogenization processes to obtain the composites’ averaged mechanical properties and isotropic response). Finite element methods can also be used to solve the elastic problem locally; however, it is not only an approximation but also it is based on the superposition approach and thus the weak solution to the elastic problem. Therefore, the deformation and strain fields determined using this method lack the degree of precision to locally assess the kinematics of the specimen under unconfined compression testing. For this investigation, a new modified mathematical approach is proposed that solves the partial differential equations of elasticity for both constituents i.e. isotropic (matrix region) and transverse isotropic (fiber region) in order to accurately represent the strain fields internally within the two main regions in the composite. The strain field is thus obtained via analytic solutions through the process of solving the elastic problem at each region locally from the microscale (at the fiber level) to the macroscale (composite specimen level) with the boundary conditions being determined experimentally beforehand; the internal strain field is solved only using the external deformation of the composite.