No sustainable development can be achieved or have any real meaning if it does not promote the use of local materials. In the northern regions of West Africa, one of the potentials to be developed for the benefit of construction is the use of Borassus aethiopum mart fibers (BAMF). The aim of this work is to estimate the elastic characteristics of mortars reinforced with Borassus aethiopum mart fibers to encourage the use of this material. To achieve this, we formulated a cement mortar, in accordance with the requirements of standard EN 196-1, reinforced with 10% Borassus aethiopum mart fibers, in volume fraction. The reference mortar is denoted M0, while the mortar reinforced with BAMF is denoted MB. The characteristics were estimated using the homogenization formula (HF) and the Hashin-Shtrikman upper and lower bounds. The characteristics of the mortar and the Borassus aethiopum mart fibers were determined before they were considered in the composite material characterization model. The results of the study show that the Hashin-Shtrikman bounds have acceptable values for limiting the range of validity of the elastic characteristics of the material. The homogenization formula proposes an increased value for the elastic characteristics of composite materials, although it still gives an idea. The Hashin-Shtrikman HS+ upper bound gives the most acceptable value for Young’s modulus of elasticity, which is 22.11GPa for a Poisson’s ratio of 0.15.