The time-dependent voltage across the pick-up electrodes of a four point probe has been determined analytically for a transient current pulse injected into a thick conductive plate modeled as a half-space. This is a step towards analyzing more complex transient four point probe signals from measurements on inhomogeneous conductors. Potential applications include the evaluation of depth-dependent conductivity profiles in metals and semiconductors. The analysis of homogeneous conductors shows how the signals are characterized by a time constant of the drive current and additional time constants dependent on the electromagnetic material properties and electrode spacings