A flat annular interfacial crack between dissimilar magnetoelectroelastic layers subjected to magnetoelectroelastic loads is investigated under the boundary condition of magnetoelectrically impermeability on the crack surface. Using the Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The field intensity factor and energy release rate are determined. Numerical results reveal the effects of electric or magnetic loadings and material parameters of composites on crack propagation and growth. The results seem useful for the design of magnetoelectroelastic composite structures and devices of high performance.