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The method of approximate product integration is applied to solve numerically the integral equations of the total currents on the surfaces of the finite tubular cylinder with complete generality both in radius and length. Procedures have been devised to take care of the squareroot singularity of the transverse total current at the end of the cylinder. Both total currents and scattering cross sections are presented for three special cases with ka = 1.0 and kh = 0.5π, 1.0π, and 1.5π. A complete set of the computer program in Fortran 4 has been prepared for the IBM 7094 at Harvard Computing Center. It can solve simultaneously for cylinders of the same radius but discrete and different lengths.