Abstract: A composite material tube, substantially insensitive to the variations of elongation under the effect of the internal pressure, comprising a number n of stable layers of reinforcement fibers, the fibers of each layer (i) being placed at the same winding angle in absolute value, referenced theta, with respect to the axis of the tube with an equal proportion of fibers wound at said angle in one direction (.vertline.theta.vertline.) as fibers wound in the opposite direction (-.vertline.theta.vertline.), the fibers of each layer being buried in a matrix which adheres to these fibers. The fibers of the same layer and the associated matrix have a volume referenced Y, the parallel fibers of the same layer and the associated matrix having overall a modulus of elasticity in the natural direction of the fibers, referenced E, wherein said n layers of fibers comply as a whole with the following relationship:0.35.ltoreq.A.ltoreq.0.