We demonstrate that hydromagnetic acceleration can be the driving mechanism of outflows in GRB sources. Using semianalytical solutions of the full set of the steady, axisymmetric, ideal hydromagnetic equations in flat spacetime -- i.e., solving the momentum equation along the flow as well as in the transfield direction -- we model the acceleration of the baryon/e±/photon fluid that emanates from a stellar-mass compact object/debris-disk system. We prove that for highly relativistic, multiple-shell outflows one can study the motion of each shell using steady-state equations. Employing a radially self-similar model, we find that the flow is initially thermally and subsequently magnetically accelerated. The Lorentz force is capable of transferring close to a half of the total energy of an initially Poynting-dominated flow to baryonic kinetic energy.