The invention is related to an apparatus and a method for processing a surface of a substrate by exposing the surface of the substrate to alternating surface reactions of at least a first starting material and a second starting material according to the principles of atomic layer deposition method. According to the invention a first starting material is fed on the surface of the substrate locally by means of a source by moving the source in relation to the substrate, and the surface of the substrate processed with the first starting material is exposed to a second starting material present in the atmosphere surrounding the source.