A sole-support device for ski bindings which includes a support member fastenable on a ski and an endless band guided transversely with respect to the longitudinal direction of the ski in a groove of the support member. In order to prevent in this device a relative movement between the upper strand of the band and the underside of the sole of the boot, the invention provides that the band, which is supported with its upper strand in the groove of the support member, has the shape of the jacket of a frustrum, and that the groove, in which the upper strand of the band is guided, has a circular extent arched toward the tip of the ski, viewed in a top view.