In this research, a fiber reinforced composite rod fixed from one end, while the other end is left free and subjected to a torsional excitation and freely vibrates. A fiber volume fraction of 40% is considered to rod of interest. Four various fibers and four matrices are taken to construct the rod in order to introduce the different shear moduli and modular ratios to investigate their effects on the natural frequency under torsion. The problem is manipulated using software of Ansys V.12 adopting the element type of (beam 188). The elastic properties of the materials are determined using software of Matlab v 6.5. The results show that maximum natural frequency is at (Gf/Gm) of (1.86), besides the results has shown that the matrix shear modulus has the most prominent effect on the natural frequency. A comparison is made between the results obtained numerically and these calculated by the exact analytical solution. A good and reasonable convergence between them is found ranging from 82.58% up to 85.59%.