The stabilizing effect of a sheared axial flow is investigated in the ZaP Flow Z-pinch experiment at the University of Washington. Long-lived, Z-pinch plasmas are generated that are 100 cm long with a 1 cm radius and exhibit gross stability for many Alfvén transit times. Experimental measurements show a sheared flow profile that is coincident with the quiescent period during which magnetic fluctuations are diminished. The flow shear is generated with flow speeds less than the Alfvén speed. While the electrodes contact the ends of the Z-pinch, the surrounding wall is far enough from the plasma that the wall does not affect stability, as is investigated experimentally and computationally. Relations are derived for scaling the plasma to high energy density and to a fusion reactor. The sheared flow stabilized Z-pinch concept provides a compact linear system.