An integrated boundary condition of the third kind for 2D eddy current problems with a multiconnected region and the corresponding finite-element equations for a formulation of magnetic intensity H are presented. In this method, there is only one unknown per node in the problem, and only the conducting region needs to be considered. The proposed method is applied to the eddy current nondestructive test (NDT) of a tube. It is an efficient method for modeling defects of any size and any position in a pipe wall for the eddy current NDT technique. Extensive calculations reveal the important fact that remote-field eddy current NDT has equal sensitivity to interior and exterior defects even when the defects are axially aligned.>