We consider tethers pulled from vesicles that are made of a membrane embedding polymers, e.g. a partially polymerized bilayer at a low degree of polymerization, Assuming that straight polymers produce a ridge in the stressed membrane, we deal with two effects, the alignment of polymers parallel to the axis of the tether and the deformation of the initially circular cross section of the tether by the aligned polymers. Studying the cases of two or more parallel polymers and of a single polymer, we calculate the free energy and the shape of the tether. Three or more polymers can collapse the tether, depending on their ridge angle. An estimate of the energies involved suggests that the stretching of polymers by tethers is practicable.