To determine the effective elastic properties of a polymer reinforced with aligned carbon nanocoils (CNCs), the finite element analysis were performed using a three-dimensional unit cell model. The coil morphology of CNCs was examined using a scanning electron microscope. The effects of coil diameter, tube diameter, coil pitch and number of coil turns on the effective elastic properties are discussed. The geometrical parameters of CNCs have a slight effect on the effective elastic properties of the material. The effective elastic properties of a polymer reinforced with randomly oriented CNCs were also predicted by the results for unit cell model. The results demonstrate that improvements in the mechanical behavior of polymers are attained through the addition of CNCs as a reinforcing phase.