A method accurately monitors the progress of polishing and accurately detects the polishing end point. The method includes directing light to the substrate during polishing of the substrate, receiving reflected light from the substrate, measuring an intensity of the reflected light at each wavelength, and producing a spectrum indicating a relationship between intensity and wavelength from measured values of the intensity. The method also includes calculating an amount of change in the spectrum per predetermined time, integrating the amount of change in the spectrum with respect to polishing time to obtain an amount of cumulative change in the spectrum, and monitoring the progress of polishing of the substrate based on the amount of cumulative change in the spectrum.