An equation of motion governing lateral deflection, considering elastic, dynamic, and drag forces is derived. This equation is applied to three different classes of drill string behavior: a beam with constant axial tension, a perfectly flexible cable, and a beam with linearly varying axial tension. Each equation is solved for the case of simple harmonic motion. A typical deep-water drill string is synthesized by subdivision into short beam sections at the top and bottom, joined by a flexible cable in the center. The lateral deflection of the drill string is obtained by joining the beam and cable solutions, subject to boundary conditions at each junction. The drill string considered is displaced harmonically at the surface by the ship and is built-in at the ocean floor. The deflection mode shapes are plotted and analyzed. The bending stresses at the top of the drill string are computed and compared with values observed under similar, conditions; the bending stresses in the vicinity of the ocean floor are also plotted.