In this study, a finite element model of a representative volume element that contains a hollow and filled single-walled Carbon nanotube (SWCNT) in two case studies was generated. It was assumed that the nanocomposites have geometric periodicity with respect to local length scale and the elastic properties can be represented by those of the representative volume element (RVE). Elastic properties in agreement with existing literature values for the Carbon nanotube and the matrix were assigned. Then for the two case studies, the tensile test was simulated to find the effect of the geometry, i.e. the volume fraction of matrix and SWCNT's properties variation, on the effective Young's modulus of the structure. In another approach, by applying perpendicular loading to the tube direction, the effect of matrix volume fraction on the transverse Young's modulus was studied. The investigations showed that for both RVEs with filled SWCNT and hollow SWCNT, the effective Young's modulus of the structure decreases approximately linear as the matrix volume fraction increases. The value of Young's modulus of the RVE with a filled Carbon nanotube was obtained to be higher than the RVE with the hollow Carbon nanotube. In addition, by increasing the tube diameter, the effective Young's modulus of the structure increases and the transverse Young's modulus decreases approximately linear for filled tubes but this parameter remains rather constant in the case of the hollow tube by increasing the matrix volume fraction.