In this paper, we investigate the asymptotically Anti-de Sitter solutions of rotating
black strings coupled to Born-Infeld and Modified Maxwell non-linear electrodynamics in the
context of Einsteinian, Einsteinian cubic and Einsteinian quartic gravity. By studying the
near-horizon behavior of solutions, we find the mass parameter, surface gravity and accordingly
the Hawking temperature. We also compute the entropy, mass, angular momentum, electric charge, and
the electrostatic potential of solutions to show that, in the context of above theories and in the
presence of two mentioned non-linear electrodynamics, the first law of thermodynamics for rotating
black strings is also exactly hold. We also investigate extremality, thermal stability and phase
transition of solutions.