An EDM method wherein the surface roughness of the machined workpiece is reduced or the ratio of the removal rate to the surface roughness is increased by controlling at least one of the rate of flow of the liquid machining medium through the discharge gap and the rate of relative displacement between the tool electrode and the workpiece along the machining interface so that each individual discharge crater on the workpiece surface becomes elliptical in shape and has its major axis at least two times greater than its minor axis.