Abstract: This paper proposes a hypersingular integral equation method toanalyze the three-dimensional mixed-mode crack perpendicular to theinterface in anisotropic electromagnetoelastic (EME) bimaterials underextended electro-magneto-elastic coupled loads through theoreticalanalysis and numerical simulations. Using the Green's functions, the generalextended displacement solutions of three-dimensional mixed-mode crackmeeting the interface in anisotropic EME bimaterials under extended loads isanalyzed by the boundary element method. Then this crack problem is reduced tosolve a set of hypersingular integral equations coupled with boundaryintegral equations. The exact analytical solution of the extended singularstresses and extended stress intensity factors near the crack front areobtained. At last, a numerical method for the hypersingular integral equationfor a three-dimensional mixed-mode rectangular crack subjected to extendedloads by the body force method is proposed. Numerical solutions of theextended stress intensity factors of some examples are obtained.