Closed form formula of torsional constant for fibers whose cross section is a hypotrochoid was obtained. Complex variable techniques were used to determine the torsion property and a conformal mapping function of power series form was derived by using the method of successive approximation. Closed form formulas for bending moment of inertia were also obtained. The formulas derived here for torsional and bending behavior should have wide application in the optimal design of fiber cross section.