Current dissipation models of coronal loop heating are studied. Turbulent current dissipation is shown to lead to a time dependent process because of an enormous mass motion induced in the current layer. A stationary heating process involves only ohmic heating, which requires a large current layer. To insure MHD stability, the loop must be composed of many elements with the oppositely directed currents. A stationary current dissipation process induces the plasma motion across the magnetic field into the loop and down the loop with the speeds v ⊥ ∼ 104 cm s−1 and v ‖ ∼ 104 cm s−1, respectively. The pressure of the loop is also estimated to be proportional to the current density: p/J=6.3 × 10-8dyn/statamp.