In an electric discharge machine and machining method for processing an object through electric discharge by impressing a voltage between a processing electrode and the object, the processing electrode and object are relatively vibrated by a vibrating part using a piezoelectric element while a gap between the processing electrode and object is properly retained at all times. The electric discharge is accelerated when the gap is small, whereas the insulated state is maintained when the gap is large. This kind of condition is stably produced in accordance with a frequency of the vibration. If the frequency is set in the range of 50-500 Hz, a shortcircuit or an arc state is less likely to occur. The vibration is effective to quickly discharge processing debris at the discharging gap.