Tail Drive Shaft of a helicopter transmits torque from the main gear box to the tail rotor and in most of the helicopter designs, tail shafts are designed to work in supercritical speeds. In order to limit resonance vibrations of the tail drive shaft, dry friction dampers can be used. Therefore, in order to study the effect of dry friction damping on the response of tail drive shaft, a mathematical model is developed. The tail drive shaft is modeled as a beam by using Euler-Bernoulli beam theory. Bearings supporting the shaft structure and couplings used are represented by linear and torsional springs, respectively. The dry friction damper is located at the middle section of the shaft which is modeled by using a one-dimensional macroslip friction model with constant normal load. The partial differential equation of motion obtained is discretized by using Galerkin's Method with multiple trial functions. The resulting nonlinear ordinary differential equations are converted into a set of nonlinear algebraic equations by using harmonic balance method utilizing single harmonic. Finally, the solution of the resulting set of nonlinear algebraic equations are obtained by using Newton's method. Using the model developed effects of parameters of the friction damper on the response of the tail drive shaft are studied.