An analytic method has been developed for fast computation of the longitudinal unsteady aerodynamics of slender axisymmetric bodies. The method is anchored by two well-established theories; the embedded Newtonian theory for hypersonic speeds and the slender body theory for sonic speed. The computed pitch damping is in good-to-excellent agreement with available experimental data, and the analytic method should serve well in the preliminary design of tactical and ballistic missiles.