In this paper, a new dual boundary element formulation is presented for dynamic crack problems in finite-thickness plates under in-plane loadings. The proposed formulation is based on a first-order plate theory (Kane–Mindlin theory) taking into account a coupled out-of-plane fracture mode due to in-plane shear loading and the effect of plate thickness on stress intensity factors, which cannot be considered within the framework of the two-dimensional elastic theories. The dynamic stress intensity factors are evaluated based on the crack opening displacements. Three benchmark examples are presented including the mixed-mode fracture of a finite plate. The effect of plate thickness on the dynamic stress intensity factors is investigated. The dynamic stress intensity factors obtained using the proposed formulation are shown to be in good agreement with the results from 3D finite element simulations.