Soft tissues in general exhibit anisotropic mechanical behavior, which varies in three dimensions based on the location of the tissue in the body. In the past, there have been few attempts to numerically model tissue anisotropy using composite-based formulations (involving fibers embedded within a matrix material). However, so far, tissue anisotropy has not been modeled experimentally. In the current work, novel elastomer-based soft composite materials were developed in the form of experimental test coupons, to model the macroscopic anisotropy in tissue mechanical properties. A soft elastomer matrix was fabricated, and fibers made of a stiffer elastomer material were embedded within the matrix material to generate the test coupons. The coupons were tested on a mechanical testing machine, and the resulting stress-versus-stretch responses were studied. The fiber volume fraction (FVF), fiber spacing, and orientations were varied to estimate the changes in the mechanical responses. The mechanical behavior of the soft composites was characterized using hyperelastic material models such as Mooney-Rivlin's, Humphrey's, and Veronda-Westmann's model and also compared with the anisotropic mechanical behavior of the human skin, pelvic tissues, and brain tissues. This work lays the foundation for the experimental modelling of tissue anisotropy, which combined with microscopic studies on tissues can lead to refinements in the simulation of localized fiber distribution and orientations, and enable the development of biofidelic anisotropic tissue phantom materials for various tissue engineering and testing applications.