One of the features of a winding engine for underwater mineral resources extraction is the area near a drum in which a flat cable gets tubular shape. The flat band is deformed, acquiring additional stresses. The values of such stresses affect engine operation safety so they have to be taken into account in design. The paper presents analytic dependences in closed form to determine the stressed-deformed state of a flat rubber cable that acquires tubular shape. It is shown that the tubular shape acquired brings about an uneven distribution of tensile forces in ropes. Values of the maximum internal forces depend on both a structure of the area where the cable gets tubular shape and the cable structural features. Internal forces emerging within the most stressed extreme ropes of the flat rubber cable within the area where it gets tubular shape are proportional to ropes rigidity. The forces decrease as the area length increases and increase as the distance between the ropes grows and depend on rubber covering rigidity with relation to the cable shift and thickness. The equations produced may be of use in engineering in designing winding engines with tubular pulling device. The study done makes it possible to apply rubber cables in underwater mineral resources extraction in deep waters, improving environmental safety of mining operations.