This paper presents modeling and analysis of coiled carbon nanotube (CCNT) reinforced polymer nanocomposites. A new algorithmic representative volume element (RVE) generation method and an RVE based finite element analysis are proposed to predict the elastic properties of CCNT nanocomposites. The elastic properties of CCNT polymer nanocomposites are studied with respect to their interphase, volume fraction, orientation, number of coils and geometrical variations such as tube diameter, coil diameter and helix angle using the proposed finite element analysis. The results show that the elastic moduli of randomly and unidirectionally dispersed CCNT nanocomposites decrease when the coil tube or the coil diameter increases. In addition, reinforcement ratio increases by increasing the number of coils. It was also observed that single walled carbon nanotube (SWCNT) fillers have better reinforcement compared to CCNT inclusions with the same volume to surface area ratio.