The present invention relates to a support device, in particular for giving lumbar support, which device comprises an elastic belt provided, at its ends, with complementary closure means, and at least one elongate side reinforcing element that is fastened over the height of the belt. In characteristic manner, over a fraction of its length, the belt has elasticity that varies over the height thereof, so that extending the belt longitudinally causes the elongate reinforcing element to shift angularly towards a respective one of the ends of the belt.