On the basis of linear beam theory, the static behavior of a pipe string designed for mining manganese nodules is formulated as a singularly perturbed boundary-value problem. This problem is analyzed by the method of matched asymptotic expansions and Galerkin's method. Static pipe deflections and bending moments are evaluated for the practical range of towing speeds of the ship. The pipe deflections obtained by Galerkin's method agree well with those by the method of matched asymptotic expansions. However, it is found that Galerkin's method with the beam function is not effective in evaluating bending moments of the pipe string.