The ability of carbon nanotubes (CNTs) to consider as the strongest and stiffest elements in nanoscale composites remains a powerful motivation for the research in this area. This paper describes a finite element (FE) approach for prediction of the mechanical behavior of polypropylene (PP) matrix reinforced with single walled carbon nanotubes (SWCNTs). A representative volume element is proposed for modeling the tensile behavior of aligned CNTs/PP composites. The CNT is modeled with solid elements. Modified Morse potential is used for simulating the mechanical properties of an isolated carbon nanotube. The matrix is modeled as a continuum medium by utilizing an appropriate nonlinear material model. A cohesive zone model is assumed between the nanotube and the matrix with perfect bonding until the interfacial shear stress exceeds the bonding strength. Using the representative volume element, a unidirectional CNT/PP composite was modeled and the results were compared with corresponding rule-of-mixtures predictions. The effect of interfacial shear strength on the tensile behavior of the nanocomposite was also studied. The influence of the SWCNT within the polymer is clearly illustrated and discussed. The results showed that polymer's Young's modulus and tensile strength increase significantly in the presence of carbon nanotubes. © (2014) Trans Tech Publications.