In the paper, waves propagating in an elastic fiber-reinforced infinite plate with a direction lying in the plane of the plate were considered. It is shown that there are two independent waves. In one of them, the displacement vector is normal to the fibers, and in the other, an arbitrary direction in the plane of propagation. The second wave with a displacement vector along the fibers must have a direction of propagation normal to the fibers in the plane of the plate. The paper discusses the limitations to which the forms of these waves are exposed, as well as the corresponding reaction voltages.