Abstract: Using Somigiliana's formula, the general solutions andhypersingular integral equations for a three-dimensional impermeable crackproblem in an infinite transversely isotropic piezoelectric solid undermechanicaland electrical loads are given. The unknown functions are thediscontinuities of the elastic displacements and electrical potential of thecrack surface. Then, a numerical technique to solve the hypersingularintegral equations is proposed based on the boundary element method combined withthe finite-part integral method. Finally, a rectangular crack undermechanical tension and electrical fields is analyzed, and the numericalresults of the stress and electric displacement intensity factors arepresented. It is shown that the numerical solutions are satisfactory,which shows that thepresent approach is powerful to solve three-dimensional crack problems ofpiezoelectric materials.