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Complex potential theory is utilized to analyze the mechanics of screw dislocations on arbitrary glide planes. An analogy with airfoil theory is shown to be useful. General procedures are given for calculating stress fields and distribution functions with the aid of conformal mapping. The theory is applied to several specific problems, including dislocations on a circular glide plane, on perpendicular intersecting glide planes, and on a glide plane within a thin film. Applications to dislocation pile‐ups on neighboring glide planes are also given.