The interface crack problem in the superconducting film-substrate structure under the magnetic field is investigated. A solution of the two-dimensional magnetoelastic problem is found. It is assumed that the plane stress state of deformation prevails in the structure. We take into consideration both cases of interface crack in the film-substrate structure and the superconductor slab. The fracture behaviors are considered for the non-superconducting substrate and superconducting substrate. Based on the simple geometrical and material assumptions, we express the explicit analytical description of the stress intensity factor and energy release rate. An increase of the stress intensity factor and energy release rate with the applied field has been observed. During the field reduction, the variations of the fracture behavior exhibit a complex characteristic. In addition, the effect of the deformation of the substrate is significant. This work may provide a tool for the analysis of the mechanical instability in the film-substrate structure.