In a method of irradiating a gas cluster ion beam on a solid surface and smoothing the solid surface, the angle formed between the solid surface and the gas cluster ion beam is chosen to be between 1° and an angle less than 30°. In case the solid surface is relatively rough, the processing efficiency is raised by first irradiating a beam at an irradiation angle θ chosen to be something like 90° as a first step, and subsequently at an irradiation angle θ chosen to be 1° to less than 30° as a second step. Alternatively, the set of the aforementioned first step and second step is repeated several times.