Abstract: Aiming at the problems of the electromagnetic momentum and stress tensor in medium，and committed to the combination with the theoretical research progress in recent years，the distinction and relation for the different forms of the electromagnetic momentum and the stress tensor in medium are compared and analyzed. Their physical meaning and functions are explored according to the Maxwell equations，Lorentz force and the momentum conservation law. We try to provide the references for the related teaching and research work.

Key words: electromagnetic field, medium, electromagnetic momentum, stress tensor, Minkowski, Abraham