A method leading to an explicit evaluation of the elastic field of a planar semicoherent interface placed in a thin isotropic plate is proposed. It is assumed that the interface contains a single family of straight, periodically distributed, misfit dislocations. The known properties of continuous distributions of dislocations and periodic elastic fields in an unbounded medium are used to solve the problem. Surface stresses are cancelled from the addition of appropriate fields applying to an infinite medium. Numerical applications illustrate, for a near Sigma 9{122} semicoherent grain boundary in silicon, the dependence of the deformation field on the plate thickness and on the orientation parameters of the interface. (C) 2015 Elsevier B.V. All rights reserved.