A microwave induced plasma source includes a coaxial waveguide made up of a cylindrical outer conductor and an inner conductor which has the form of a helical coil, a discharge tube inserted into the helical coil in the axial direction thereof, and having an inner tube for introducing a sample and an outer tube for introducing a plasma gas so that a double tube structure is formed, a discharge-tube cooling device for causing a cooling gas to flow along the outer periphery of the discharge tube in directions parallel to the axis thereof, and a microwave power source for supplying microwave power to the coaxial waveguide. When the microwave induced plasma source is used as the light source of a spectrometer or the ion source of a mass spectrometer, a trace element can be readily determined qualitatively or quantitatively.