A novel numerical approach to model the bending of a straight Mallory tube into a desired configuration is described. The effect of the bimodular behavior of synthetic reinforcement cord on the bending process is reported. The reinforcement used encompasses the most widely used fibers such as polyester, nylon, and rayon. The principal strain magnitudes at the reinforcement layer are computed under pure bending. The internal inflation pressure and the angular velocity at which the tube is rotated do not have a noticeable effect on the strain magnitudes. However, the axial length of the tube, the location of the reinforcing layers inside the thickness of the tube, and the orientation of this layer have shown remarkable influence on the strain distribution. Finally, the strain magnitudes from the numerical solution are compared with the strain magnitude measured from actual photographs of the tube during testing. The calculated strain magnitudes and the measured ones were found to be in good agreement.