An array of continuously distributed screw dislocations piled up against an elliptic cylindrical rigid inclusion was analyzed. Both uniformly applied shearing load at infinity and internal stress opposing the movement of dislocations were taken into account. Based on the analogy between continuously distributed dislocations and a crack, the stress function of the pile-up problem was determined by the complex variable method in the theory of elastic cracks. The pile-up tip was assumed to be away from the matrix-inclusion interface, its distance from the interface being determined by the condition that the stress should be finite everywhere in the solid. The stresses on the interface and on the slip-plane were then calculated and some typical stress distributions were graphically shown. The condition for initial debonding of the interface was also discussed. The critical debonding load was expressed by the sum of two terms, one the friction stress and the other inversely proportional to the square-root of the slip-line length.
