2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/182457We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence and uniqueness for solutions close to a trivial solution. This trivial, or natural, solution corresponds to a stress-free body in rigid motion.12 pages, with slight corrections, to be published in Commun.Math.PhysGeneral Relativity and Quantum Cosmologytext