As a prelude of three-dimensional modeling of a submarine, an analysis of degaussing of a two-dimensional magnetic cylinder is presented in this paper. The cylinder is of infinite length and may be of arbitrary cross section. As the first step of determining the degaussing current needed for minimizing the magnetic field of the cylinder, a free surface current is assumed on the cylinder surface. Under the influence of the magnetic field produced by the assumed surface current, the cylinder is magnetized and a magnetization current is induced on its surface. An integral equation is formulated for the unknown magnetization current, with the magnetic field due to the assumed surface current as the forcing function. The integral equation is solved numerically employing the moment method. Then, based on knowledge of the magnetization current, the magnetic field produced by the cylinder is calculated. The magnetic field of the cylinder which is magnetized by the assumed surface current is compared with the field of the same cylinder but magnetized in the earth's magnetic field. The ratio of the magnetic flux density of these two fields is taken as the "scaling" factor for determining the degaussing current needed. Numerical results are presented and discussed. In particular, data for a circular cylinder are compared with the analytical results obtained based on image theory. To illustrate the effectiveness of the degaussing system, the magnetic flux density of a magnetic cylinder after applying the degaussing current on its surface is compared to that without the degaussing current.