A piezoelectric material with a Griffith crack perpendicular to the poling axis is analyzed within the framework of the theory of linear piezoelectricity. Using exact electric boundary conditions at the crack surfaces, the nonlinear behavior between the electric displacement at the crack faces and applied loading is given, and it can be approximated by a linear relation on applied electric field. The Fourier transform technique is employed to reduce the mixed boundary value problem to dual integral equations. Solving resulting equations, expressions for the electroelastic field in the entire plane are obtained explicitly for a cracked piezoelectric material subjected to uniform combined electromechanical loading. The distribution of asymptotic field and the intensity factors of electroelastic field as well as the elastic T-stress are determined. Particularly, the maximum hoop strain s θ θ is suggested as a fracture criterion for piezoelectric materials. Based on this criterion, relevant experimental results can be explained successfully. As an illustrative example, theoretical predictions for PZT-4 ceramic with a crack are in excellent agreement with existing experimental data, not only in qualitative behavior but also in quantitative results.