The effects of the argon gas pressure, charging voltage and anode shape on the current sheath dynamics in a low energy (4.9 kJ) Mather type plasma focus (PF) were investigated. The formation and dynamics of the current sheath were monitored by using two magnetic probes, which were inserted radially and axially to explore the evolution of the plasma sheath and to estimate the range of its velocity during the break-down and run-down phases. The radial magnetic probe measurements showed a rather constant current sheath velocity near the insulator, which was more sensitive to the variations of the gas pressure than the charging voltage, and the current sheath did not lose its uniformity by expanding away from the insulator during the break-down phase. The results found from the axial magnetic probe signals revealed a higher current sheath velocity inside the step region of the step anode than the cylindrical one. The simulated axial current sheath trajectories (Lee's model) that were obtained after the fitting process of the current signals showed good agreement both for the cylindrical anode throughout the run-down phase and the step anode before the step region. Inside the step region, the separation between the simulated and the experimental trajectories of the step anode was increased at greater axial distances.