In this study, the mechanical properties of graphene and single walled carbon nanotubes (SWCNTs) were investigated based on molecular dynamics (MD) simulation. During the characterization of the mechanical properties, the atomistic interactions of the carbon atoms were described using the bonded and non-bonded energies. The bonded energy consists of four different interactions: Bond stretching, bond angle bending, dihedral angle torsion, and inversion. On the other hand, the non-bonded interaction between the carbon atoms within the cut-off ranges was regarded as the van der Waals (vdW) force. The effect of vdW force on the mechanical properties of graphene and SWCNTs would be mainly of concern. Simulation results indicated that the Young's modulus of the graphene with vdW force included is 15% higher than that without considering any vdW interaction. The same tendency also was observed in the armchair and zig-zag SWCNTs. Furthermore, it was revealed that the increment of moduli caused by the vdW force could be primarily attributed to the 1-4 vdW interaction. The influence of the vdW interactions on the mechanical properties of graphene and SWCNTs was then elucidated using the parallel spring concept.