This research develops transfer matrix model for the longitudinal vibratory component of a rotary-vibratory drilling (RVD) system driven with an electrohydraulic inertial mass exciter. The RVD system is a hybrid drilling system consisting of a conventional rotary drilling system assisted by forced harmonic vibrations. The model includes a drill string with continuously distributed inertia, stiffness, internal material, and external fluid damping. These properties were introduced through a new continuum transfer matrix for a damped pipe element. The model allows for the inclusion of realistic geometrical representations for the drill string, and the inclusion of masses, springs, dashpots, and other axial structural elements. The force exerted on the drill string by the drilling fluid was included using the theory of a flat plate oscillating in a newtonian fluid. The force had an inertia and a viscous damping component. These were incorporated into the inertia and external fluid damping terms in the new continuum transfer matrix. The exciter had force and power limits. The rock-rock bit boundary was represented as a structurally damped spring. / Ph. D.