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Along the two contours of a doubly connected region, mixed boundary values of slipless nature are prescribed. The problem is formulated on a complex z-plane in terms of a Hilbert functional equation involving a holomorphic function φ(z). Based on plane theory of elasticity, the solution is found in the form of a double series. An effective method of successive approximation is shown for the computation of the coefficients of the series. Numerical examples of the field of stress and deformation are illustrated with diagrams. By superposition, the solution presented can be used to solve another class of mixed problems in elasticity involving frictionless indentation.

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