Twining plants use their helical stems to clasp supports and to generate a squeezing force providing stability against gravity. To elucidate the mechanism that allows force generation we measured the squeezing forces exerted by the twiner Dioscorea bulbifera while following its growth using time-lapse photography. We show that the development of the squeezing force is accompanied by stiffening of the stem and the expansion of stipules at the leaf base. We use a simple thin rod model to show that despite their small size and sparse distribution stipules impose a stem deformation sufficient to account for the measured squeezing force. We further demonstrate that tensioning of the stem helix although counter-intuitive is the most effective mechanism for generating large squeezing forces in twining plants. Our observations and model point to a general mechanism for the generation of the twining force: a modest radial stem expansion during primary growth or the growth of lateral structures such as leaf bases causes a delayed stem tensioning that creates the squeezing forces necessary for twining plants to ascend their supports. Our study thus provides the long-sought answer to the question of how twining plants ascend smooth supports without the use of adhesive or hook-like structures.