Dissimilar orthotropic stiffness coefficient variations are a characteristic feature of unidirectionally reinforced fiber composites with a variable fiber volume fraction, but have not been commonly considered in the literature. The objective of this work is to account for them and obtain a three-dimensional elasticity solution with specific reference to simply supported rectangular plates. The analysis involves the solution of variable coefficient governing equations using the power series approach. For a graphite–epoxy plate with a sandwich-like configuration, results useful as a benchmark for future comparisons are tabulated for a specific power law variation of the volume fraction. It is shown that the thickness-wise variations of displacements and stresses are significantly nonlinear, and such variations are not captured correctly by the classical plate theory. Further, on the basis of the elasticity solution, the relative benefit of using a sandwich-like configuration versus a homogeneous plate is shown to depend on the span-to-thickness ratio and to decrease significantly as the plate becomes thick. © 2018, Springer-Verlag GmbH Austria, part of Springer Nature.