In this study the derivation of the most general equilibrium and shear stress expressions for transversely isotropic fiber composite bar were theoretically investigated with the coordinate parameters of torsion problem. Nonlinear governing equations were modified in a linear system of differential equations by the application of assumptions. Equilibrium equation was separated into three different term-parts in terms of the uncoupled forms of the stress and warping functions. Derived resultant expressions have shown that the total number of independent elastic constants are reduced from twenty-one to five. Coordinate dependent variances of two shear stresses were presented on the transverse and lateral cross sections of fiber composite cylindrical bar in terms of the five unknown elastic constants.