It is important that copper films fill the sub-micron trenches on silicon substrates in order to produce high-density electronic devices. In this paper, changes of the copper film profiles in trenches on silicon substrates during the reflow process were numerically calculated by 2- and 3-dimensional analyses. Calculation results from a model of atomic surface diffusion in a thin layer on the film were similar to experimental results. The relationship between the change of the film profile and the geometric parameters was determined. The results show that a uniform and thick initial film on the side walls of a trench is important to avoid film-bridge and void formation in the trench. In order to increase flow rate into the trenches, narrow trenches with a thick initial film on the bottom of the trench are effective.