The conductance of sodium ions through a simplified channel-membrane system immersed in a reservoir of 1M NaCl in SPC/E water is examined by molecular dynamics simulation. An applied external potential of 1.1 V drives the ions and water through a channel of length 25 A producing a current of 19.6 pA, in reasonable agreement with experimental findings. The stream of ions and water molecules flows continuously because of the constant applied field and periodic boundary conditions. We also examine the potential profile across the simulation cell, the average density distributions of the various species in the reservoir and radially in the channel, and the ion velocity in the channel.