To obtain the simulated eddy current testing (ECT) signals of steam generator (SG) in nuclear power plant (NPP), nodal-based finite element (FE) analysis with magnetic vector potential (MVP) is usually used. To perform the numerical analysis, we derive the governing equation in terms of MVP and electric scalar potential (ESP) from Maxwell’s equations. To insure the uniqueness of solution, gauge condition has to be considered. In eddy current problems, Coulomb gauge condition (CGC) is usually used. In 2-D or 3-D axis-symmetric analysis, CGC is included during formulation and ESP is eliminated using some special assumption. Because CGC is not used during the formulation in 3-D analysis, we have to include artificially. And because of the heavy computation cost for 3-D analysis modified magnetic vector potential (MMVP) is used by elimination ESP. In this paper, effects of artificial treatment of CGC and elimination of ESP on ECT signal are investigated in order to help for obtaining accurate numerical simulation results.