This paper considers the influence of Maxwell stress on a penny-shaped crack in a 3D piezoelectric material under combined mechanical and electric loadings at infinity,where the crack is assumed to be the electrically semi-permeable.Based on the displacement discontinuity boundary integral equation method,the relationships among the strip zone,the applied mechanical and electric loadings,the intensity factors of stresses and electric displacement and the local J-integral are derived,respectively.Numerical results are also given to discuss the effects of Maxwell stress on the intensity factors of stresses,the electric displacement and the size of the electrically yielded zone.The normalized stress intensity factor always increases as the applied mechanical loadings or the applied electric loadings increase.It is found that the Maxwell stress can enhance the crack growth under a given mechanical and electric loading.Especially for the case of low mechanical loading and high electric loading applied at infinity,the Maxwell stress has great influence on the normalized stress intensity factor,the electrically yielded zone and the electric displacement in the crack cavity.