The force necessary to break the adhesive bond of a single fiber from a multilayer composite is investigated. An important application of this analysis is the determination of the force required to pull the wire-guided fiber from the wound spool of a missile as it deploys the control fiber in flight. Deformations of the pulled fiber include bending, stretching, and torsion. The equilibrium equations are similar to the equation that governs a beam on an elastic foundation except that the three equations are coupled. A closed-form solution to the equilibrium equations is obtained with the constants of integration evaluated by carefully applying the appropriate boundary conditions. Results obtained include the variation of debonding force with the pulling angle, the transition of the governing failure mode of the adhesive layers, and the stress distributions in the adhesive layers. Results obtained for a special case of the double-cantilever beam are in excellent agreement with results in the literature.