Abstract: A machine for winding shells with convex ends on mandrels using thread such as resin-impregnated fibreglass threads comprises a mechanism for rotating the mandrel around its longitudinal axis, a thread guide installed on a traverse carriage located on a horizontal guide, and a mechanism for moving the carriage over the horizontal guide. The thread guide is mounted on the carriage with a provision for moving relative to it in the direction perpendicular to the mandrel axis. The horizontal guide is arranged parallel to the mandrel axis. The mechanism for moving the carriage along the horizontal guide includes of an endless flexible linkage whose position is space is set by master guide; the shape of these master guides in the rectangular system of coordinates x, y depends on the relation: ##EQU1## The flexible linkage is connected with the mandrel-rotating mechanism and with the traverse on which the thread guide is mounted.