Elastic wave transmission characteristics through a fiber-reinforced composite layer are studied by the two-dimensional steady-state finite element analysis. To this purpose, boundary conditions are formulated which account for the connection of the model domain to the semi-infinite regions as well as a certain periodicity of the fiber arrangement. The transmission characteristics through a composite layer are computed for the longitudinal and transverse wave incidence, assuming a finite number of fiber alignments in a square array. The analysis delineates the existence of clear stop bands in the case of transverse wave incidence, even with a few lines of fibers aligned normal to the propagation direction. These stop bands are discussed on the basis of the interference effects of neighboring fiber alignments as well as neighboring fibers in each alignment.