Abstract: By using the basic displacements and stresses caused by a single elastic inclusionand a single crack on infinite plane,the interaction problem between a crack and anelastic inclusion is reduced io solve a set of Cauchy-type singular integral equation.Based on this result,the singular behaviour of the solution for the inclusion-branchingcrack is analysed theoretically and the oscillating singular interface stress field isobtained. For the separating inclusion-crack problem,the stress intensity factors at thetips and the interface stress of the inclusion are calculated and the results of which aresatisfactory.