Abstract: This work presents a wave time-domain hypersingularintegral equation (WTD-HIE) method proposed by the authors for modeling 3Dcrack propagation problem on co-seismic slip under fully coupledelectromagnetothermoelastic P- and S- wave fields through theoretical analysisand numerical simulations. First, the general extended incrementaldisplacement wave solutions are obtained by wave time-domain Green'sfunction method. Then, based on the nonlinear boundary element method, theproblem is reduced to solving a set of WTD-HIEs coupled with nonlinearboundary integral equations, in which the unknown functions are the generalextended displacement discontinuity waves. The behavior of the generalextended singular stress indices around the crack front terminating at theslip surface is analyzed by the time-domain main-part analysis method. Thegeneral extended incremental singular stress waves and the extended stressintensity factors are obtained by closed-form solutions. In addition, anumerical method for the problem is put forward with the extendedincremental displacement discontinuity waves approximated by the product oftime-domain basic density functions and polynomials. Finally, extendedstress intensity factors radiation distribution for P- and S- waves at the cracksurface are calculated, and the results are presented to demonstrate theapplicability of the proposed method.