We have used a quartz tube 10.8 cm long, 2.8 cm in internal diameter and 1 mm in wall thickness and produced the pinch effect by current in an axial direction in pre-ionized plasma. Before the gas was ionized, a magnetic field in the axial direction was produced by external coils. The following magnitudes are typical: duration of pulse, 25 mμsec; potential difference between the electrodes, 20 kV; current through the tube, 30 kA; gas pressure before ionization 50 mtorr. Measurements were made of the potential difference between the electrodes, the current through the tube and the magnetic field within the tube in both the θ and z directions. It was found that the current skin thickness (3—4 mm) was much larger than any existing theory predicts. A theory based on the assumption that the drift velocity of the electrons is limited by "streaming" instabilities is developed. This theory explains most although not all of the experimental results.