We characterize Lorentzian submanifolds by using non-null hyperelastic curves along a Lorentzian immersion defined between suitable two Lorentzian manifolds. We introduce a Lorentzian hyperelastic immersion as a map that carries a hyperelastic curve in the submanifold to a hyperelastic curve in the ambient manifold by the isometric immersion theory. Then, we investigate the characterization of submanifolds by using hyperelastic curves along Lorentzian immersions. Also, we exemplify the findings.