Natural-fiber-reinforced composites are seen as a good alternative to traditional synthetic-fiber composites. However, to successfully implement these materials in engineering applications, along with these materials demonstrating satisfactory load-bearing capacity, it is necessary to provide engineers with effective material properties, as well as calculation methods that take into account the distinctive features of natural fibers. This study investigated the effective elastic properties and strength of materials composed of unidirectional sisal fibers within a thermosetting polymer matrix, containing 20%, 40% and 60% fiber-volume fraction. Experiments with axial and off-axis loads in conjunction with finite-element modeling were utilized to determine the effective mechanical response of the composites. Analytical and numerical models were considered, using both isotropic- and anisotropic-fiber approaches. It is shown that only by taking into account the sisal-fiber anisotropy can the experimental results of the off-axis experiments be reproduced. The influence of sisal-fiber transverse modulus on the overall mechanical response is a function of the sisal-fiber volume fraction. It has been shown that the longitudinal specific strength of sisal-fiber-reinforced composites is comparable to classical aluminum alloys or steel. Thus, this environmentally friendly composite can be considered as an alternative in some engineering applications, such as reinforcement in concrete composites.