This work presents hypersingular integral equation methodto analyze the multiple three-dimensional cracks problem in fully coupledelectromagnetothermoelastic multiphase composites under extendedelectro-magneto-thermo-elastic coupled loading through intricate theoreticalanalysis and numerical simulations. First, the problem is reduced to solvinga set of hypersingular integral equations. Analytical solutions for theextended singular stresses, the extended stress intensity factors, theextended strain energy factors and the extended energy release rate near thecracks front are obtained, respectively. Then, the numerical method for thehypersingular integral equations subjected to extended coupled loads isproposed. Finally, numerical solutions of the extended stress intensityfactors and the extended strain energy factors for two interactingthree-dimensional cracks are given, and the effect of cracks orientation,interaction and shielding is discussed.