Quantum mechanical tunneling through insulating barriers has received considerable attention in recent years, especially in metal-insulator-metal systems and p− n junctions. It is the purpose of this paper to discuss tunneling in the MIS contact. In this paper we define the d.c. currents which flow and then calculate the voltage distribution in the contact. It is found that as long as the semiconductor spacecharge region is of the order of the insulator thickness (∼ 50 Å) considerable voltage drops across the semiconductor. Using this, a voltage region of low conductance is shown to exist, over which the metal Fermi level is opposite the forbidden gap of the semiconductor. This region is shown to be greater than the semiconductor energy gap. In addition, the a.c. frequency dependent currents which flow in an MIS contact due to interface states are calculated. It is shown that interface states can contribute to the a.c. conductance via two mechanisms; time lag in trapping and recombination of carriers in the semiconductor bands and tunneling via interface states. Both of these mechanisms are discussed and the conditions under which one or the other make the major contribution to the a.c. conductance is analyzed.