Although the leakage flow through labyrinth seals under stationary conditions has been examined by many investigators a reliable prediction of the effect of various labyrinth parameters on leakage rate has not been reported so far. The theoretical models for the seals proposed in most of the previous literature provided results with considerable differences and contradictions in some cases. The structure of the laminar incompressible flow and the performance of a number of seals of various shapes for both stationary and rotating conditions are investigated in this paper. The theoretical treatment is based on the formulation of three-dimensional axisymmetric momentum and continuity equations for labyrinth shapes having small height to radius ratio as is always the case in turbomachinery, rotodynamic pumps and many hydraulic devices. It is found in this paper that shaft rotation is only beneficial for the up-the-step seal, has no effect on grooved shaft and grooved casing seals and has an adverse effect on the down-the-step seal. It is also found that the use of a smaller clearance size at the entrance makes some improvement in the performance of the grooved shaft and down-the-step seals depending on the value of the height to width ratio of the seal.