The properties of the Fourier series and the method of their application are reviewed here. The treatment of Fourier's method of analysis is not a new problem, there have been but a comparatively small number of studies that have been made using this method. These have been reported since the proposition was made by B.L. Averbach and B.E. Warren in 1949. Recently the extensive use of electronic computors has made this method popular in the field of engineering for the purpose of studying the strength of materials. The summary of the discussions on this method will be introduced here.