Closed form solutions for torsional rigidity and the torsional shape factor for fibers whose cross section is a generalized cardioid are obtained. Complex variable techniques are used to solve the torsional problem, and a conformal mapping function is derived using the method of successive approximation. Closed form solutions for bending rigidity and bending shape factor are also obtained with Green's theorem. The expression for the perimeter for a generalized cardioid is found. Expressions derived here for torsional and bending behavior should have wide applications in the optimal design of fiber cross sections.