Abstract: An electroelastic analysis is performed on a transverselyisotropic material containing elliptic hole, which subject to a uniformstress field \sigma ^\infty and a uniform electric displacement fieldD^\infty at infinity while the surface of the hole is free of tractionand electrically open. Taking PZT-4 ceramic into consideration, the resultsbased on the exact electric boundary conditions and the impermeable electricboundary conditions are all obtained. It can be seen that the relatedresults of these two electric boundary conditions are entirely identicalwhen the hole is a circular hole. The impermeable electric boundarycondition is becoming incorrect with the elliptic hole degenerating into acrack. A comparison between these present results and the related resultsshows that the present results are validity. It also shows that some resultsgiven by Sosa are incorrect maybe due to his calculation, not theimpermeable electric boundary.