The present work is concerned with an extension of the Castigliano s theorem to the case of inelastic damageable trusses (elasto-plastic and elasto-viscoplastic behavior). A general formulation that takes into account any kind of constitutive theory with internal variables is presented. A numerical technique, based on the operator splitting method, for approximating the resulting equations is proposed. Finally, the proposed theory is checked through examples concerning cyclic and monotone loadings in metallic trusses.