It is necessary to find out whether there are metal defects on underground gas distribution pipelines without excavation in order to establish safety strategies for replacement or maintenance. The metal defects are classified into general corrosion, stress corrosion, cracking, lamination, pits, and metal loss, which cause leak or partial damages to a gas pipeline. Therefore, it is required to develop an effective method in the form of an in-line inspection concept that could be implemented internally into a gas pipeline. In this study, theoretical formulations of the magnetic vector potential and magnetic flux density including axial and radial wave numbers based on Maxwell equations are presented analytically to find out the changes of amplitude and phase in the magnetic flux density and the consequent induced voltage which can be a criterion in the remote field eddy current principle for detecting the metal defects in gas pipelines. Three-dimensional finite-element analysis is also presented to analyze the physical phenomenon in metal defects according to each defect size, excitation frequency and moving velocity, which can overcome inaccuracy of the two-dimensional approach, using axisymmetry condition, and simulate local pit conditions occurred severely in real gas pipelines; otherwise only metal loss such as whole circumferential decrease in wall thickness can be modeled. Some experimental works are performed to validate the analytical and finite elemental results regarding the magnetic flux density and induced voltage in the detector.