Our literature search revealed only a modest amount of research has been devoted to the specific problem of quantifying micromechanical stress distributions in fibrous composites. Most of what is available deal with the simple situation of unidirectionally reinforced composites with straight fibers and subjected to static axial loads; see for example [1–7]. For further references we refer the reader to McCartney’s paper [6] for more recent works and to Nayfeh’s paper [7] for previous literature. Comparatively speaking, less work has been carried out on similar problems involving dynamic loading. Here, however, there exists a reasonable body of research on wave propagation interaction with fibrous composites, the interest of which is mainly concerned with the dispersive characteristics of such classes of materials (see, for example, [8]).