This study investigates the two-dimensional static mechanics of an axially moving cable used in a two-ship continuous line bucket (CLB) system for exploiting mineral resources deposited on the sea floor. The aim of this study is to formulate a theory for estimating the grounding length of the cable. The theory is governed by the relation for the static equilibrium of forces acting on the cable and geometrical conditions imposed on the submerged length of the cable and on the distance between the two ships supporting the cable. Two algorithms involving a couple of iterations are developed for obtaining the grounding length. The calculation using the algorithm shows that the grounding length varies in response to changes in the rate of collection by the bucket and the bucket interval. The calculation also demonstrates that the maximum grounding length is determined on the basis of the geometry of the submerged part and that the grounding length ranges from zero to the maximum depending on the distance between the two ships.