This paper extends the application of the finite element method of lines (FEMOL) to elastic bodies of revolution under arbitrary loads The loads are expanded into the Fourier series in the circumferential direction and the problem is then reduced to a series of two dimensional problems are constructed, corresponding systems of ordinary differential equations are derived and the singularity at r=0 due to the use of cylindrical coordinates is reasonably treated and removed Numerical examples are given in the paper to show the outstanding performance of the proposed method