Finite element analysis was implemented to evaluate the transverse shear modulus of a unidirectional glass/epoxy fiber-matrix composite based on pure shear displacement boundary conditions. Unit cells consisting of three-dimensional glass cylinders surrounded in square-cuboid epoxy matrices were modeled to represent "Representative Volume Element" (RVE) configurations in periodic and random-periodic square cell arrangements of variable size. Three RVEs were constructed and analyzed: A single unit cell, a 9-cell (3 x 3) array, and a 25-cell (5 x 5) array. Additionally, the unit cell was modeled to include an interphase. Three sets of cell arrangements were constructed and evaluated: a periodic square array, a transversely distributed random-periodic array, and a variable angularly aligned random-periodic array. Furthermore, scale and free-edge effects of the composites were studied by evaluating the shear modulus in incrementally increasing domains, as well as by isolating finite-sized domains called windows within the multiple-cell model, whereby the window is smaller than the array. Finite element software was subsequently utilized to create a three-dimensional mesh of the composite models studied. Each simulation consisted of exposing the respective domain to pure shear boundary conditions, whereby the model was subject to uniform transverse displacement along its boundary. Subsequent volumetric averaging resulted in computation of the apparent transverse shear modulus. The resulting numerically attained elastic shear modulus was then evaluated and compared to known predictive models in literature. It was shown that that the transverse random arrangement as well the random angular alignment of fibers within the composite structure had a marginal influence on the shear modulus. For random transverse distributions, a deviation in modulus of +1.5% was observed for the 25-cell array as compared to a periodic array of equal size. Similarly, a deviation of +0.3% was predicted for 25-cell arrays subject to random angular fiber misalignments up to ±0.143°, as compared 25-cell periodic arrays. Furthermore, increasing the composite medium by systematic, incremental augmentation model domains was shown to significantly lower the shear modulus in a convergent manner as G23 values dropped 33.5% from the nonhomogeneous single cell to the 9-cell model, and 2.6% from the same 9-cell to the 25-cell model, while observing the effects of a mesoscale window displayed little variance in modulus value as compared to the larger RVE from which the window was isolated from. Lastly, the predictive potential of the model developed by Sutcu for composites with interphases, and other commonly employed models for predicting the transverse shear modulus of unidirectional composites was also evaluated. Numerical results of nonhomogeneous interphase models for both periodic and random-periodic 25-cell arrays were found to be in excellent agreement with Sutcu's approximation. The shear modulus of the 25-cell, nonhomogeneous interphase model was found to lie within 3.5% of Sutcu's prediction. Volume averages for periodic arrays with no interphase were observed to lie in close proximity to Halpin-Tsai's model, displaying a variation of 7% for a 25-cell, single fiber model.