The purpose of this paper is to investigate the mechanical behavior of fiber-reinforced incompressible nonlinearly elastic solids under large simple shear deformations. Two different rubberlike materials, with distinct properties of adhesion, were reinforced by a single family of parallel fibers of nylon. Fibers of nylon 6 monofilament fishing line with diameters of 0.25, 0.45, and 0.80 mm were used. Fiber-reinforced specimens were tested under monotonic load at constant temperature, and values of amount of shear were obtained by the digital image correlation method. A phenomenological constitutive model is proposed to predict the mechanical behavior of the transversely isotropic materials. The proposed model takes into account the shear and stretch in the fiber, and fiber-matrix iterations. These iterations are related to the quality of the fiber-matrix bonding and fibers pullout. The obtained results can be useful in understanding the mechanical behavior of fiber-reinforced rubberlike solids and fibrous soft tissues.