Abstract: The anti-plane problem for a functionally gradient magneto-electro-elastic strip containing multiple collinear cracks perpendicular to the boundary is investigated. The cracks are assumed to be either magneto-electrically impermeable or magneto-electrically permeable. Integral transforms and dislocation density functions are employed to reduce the problem to Cauchy singular integral equations. Field intensity factors and energy release rate are derived, analyzed and calculated numerically. The numerical results show the effect of the parameters of loading combination, the material gradient indices and the crack configuration on the fracture behavior of the cracks.