As a part of the efforts towards a professional and reliable numerical tool for resistance welding engineers, this Ph.D. project is dedicated to refining the numerical models related to the interface behavior. An FE algorithm for the contact problems in resistance welding has been developed in this work, dealing with the coupled mechanical-electrical-thermal contact problems. The penalty method is used to impose the contact conditions in the electrical and thermal contact, as well as frictionless contact and sticking contact in the mechanical model. A node-segment contact element is the basis for the formulation, and the interfaces are treated in a symmetric pattern. The frictional sliding contact is also solved employing the constant friction model. The algorithm is incorporated into the finite element code. Verification is carried out in some numerical tests as well as experiments such as upsetting together two or three cylindrical parts as well as disc-ring pairs of dissimilar metals. The tests have demonstrated the effectiveness of the model. A theoretical and experimental study is performed on the contact resistance aiming at a more reliable model for numerical simulation of resistance welding. The model currently employed is evaluated. It is found that the model may underestimate the constriction resistance because it is based on the assumption of continual contact area. A new model is proposed on the constriction resistance in resistance welding. A parametric study is performed on the contact resistance with the Gleeble machine. The influence of some variables such as interface normal pressure, temperature and material properties are investigated, leading to a better understanding of the contact resistance. The models are also examined. Finally the performance of the overall contact model is validated in some projection welding experiments. The program is also applied to solve some resistance welding operations involving contact problems, showing that numerical simulation facilitates better understand of resistance welding.