A machining apparatus capable of easily machining a workpiece to reproduce a shape of a machining model or with alternation of a scale in a scanning or profiling direction. A non-contact displacement gauge is fixed to one surface of a tool rest, and a tool to the other surface. A machining model is disposed opposite to the displacement gauge, and a workpiece opposite to the tool. The displacement gauge measures distance to the machining model which is measured by using a probe and outputs an output signal. The output signal is amplified by using an amplifier to drive an actuator that projects the tool. The amplification degree of the amplifier is designed to be adjustable. By so doing, the workpiece can be machined with alternation of the scanning or profiling scale in relation to the machining model.