The stress distribution at the interface junction of an elastic inclusion embedded in a brittle matrix is examined. Solutions are derived for the stress and displacement fields near the junction formed by the intersection of the interfaces between the inclusion and the matrix. The stress field consists of symmetric (mode 1) and skew-symmetric (mode 11) components. The magnitude of the intensity factor associated with each mode of deformation is determined using a combination of the finite element method and a contour integral. The numerical results of the stresses near the interface junction of two different inclusion geometries show that the asymptotic, solutions of the stresses are in agreement with those from the finite element prediction when higher-order terms are considered. The implications of the results for the failure of particle-reinforced and two-phase brittle materials are discussed.