In this paper, the mode III crack intwo bonded half infinite functionally gradedmagneto-electro-elastic materials is investigated. It is assumed thatthe elastic stiffness, piezoelectric constant, and dielectricpermittivity of the magneto-electro-elastic material vary continuously alongthe thickness of the strip. The crack is assumed to be eithermagneto-electrically impermeable or permeable. Integral transformsand dislocation density functions are employed to reduce theproblem to Cauchy singular integral equations which can be solvednumerically by Gauss-Chebyshev method. Numerical results are obtainedto illustrate the variations of the stress intensity factors (SIFs)with the parameters such as material nonhomogeneityfactor, crack sizes, loading conditions, which are shown graphically.