In order to further improve the properties of composite materials, particular attention has been paid to the additional reinforcements. One of the most promising reinforcements is the carbon nanotube "CNT". Naturally, a double bound between carbon-carbon with an sp2 hybridized orbital in graphene is one of the most rigid of the bonds. The CNTs possess an ideal arrangement of these bonds in a cylindrical structure, which gives them extremely high modulus. For many researchers, it is the ideal reinforcement for new composites. Moreover, the material used in this study will be reinforced by one of the most cultivated vegetable fibers in Algeria, which is date palm fiber. In this study, the elastic modulus of a four-phase material (fiber, gmatrix, CNT, and interphase) is assessed. Firstly, an analytical approach is conducted with emphasizing on the effect of interphase thickness, intragallery enhancement factor and CNT size on nanocomposite elastic modulus. Then, a numerical study showing the effect of CNT waviness and interphase thickness on elastic modulus of the nanocomposite is conducted. The presented results show a significant effect of the abovementioned parameters on the behavior of the nanocomposite. These results give better insights into the real behavior of the nanocomposite and invite researchers to enhance the interfacial bonding of CNT/matrix and to control the undulation of CNT once embedded in a matrix. [GRAPHICS] .