In　this　paper,　the　fatigue　crack　problems　in　piezoelectric　materials　under　cyclic　mechanical　loading　or　alternating　electric　field　were　analyzed　by　a　single-domain　boundary　element　method.　To　determine　the　direction　of　the　crack　propagation,　the　fracture　criteria　of　maximum　of　hoop　mechanical　strain　energy　release　rate　was　used.　Meanwhile,　for　evaluating　the　remaining　life　of　the　cracked　piezoelectric　specimens,　the　Paris-type　laws　based　on　different　fracture　parameters　were　employed　and　compared.　All　the　involved　fracture　parameters　were　computed　by　the　interaction　integral　method.　Numerical　examples　were　considered　and　analyzed　for　cyclic　mechanical　and　electrical　loadings,　respectively.　The　comparisons　showed　the　efficiency　of　the　present　BEM　program　in　analyzing　fatigue　cracks　and　the　choice　of　the　effective　fracture　parameter　in　Paris＇　law　for　life　prediction.