Aconcurrentmultiscalemethodisdevelopedforsimulatingquasi-staticcrackpropagationinwhichthefailureprocessesoccurinonlyasmallportionofthestructure.Forthispurpose,amultiscalemodelisadoptedandbothscalesarediscretizedwithfinite-elementmeshes.Theextendedfiniteelementmethodisemployedtotakeintoaccountthepropagationofdiscontinuitiesonthefine-scalesubregions.Atthesametime,fortheothersubregions,thecoarse-scalemeshisemployedandisresolvedbyusingtheextendedmultiscalefiniteelementmethod.Severalrepresentativenumericalexamplesaregiventoverifythevalidityofthemethod.