Abstract: Based on the covariant Lagrangian function and Euler–Lagrange equation, a set of classical fluid equations for strong EM wave-spin plasma interaction is derived. Analysis shows that the relativistic effects may affect the interaction processes by three factors: the relativistic factor, the time component of four-spin, and the velocity-field coupling. This set of equations can be used to discuss the collective spin effects of relativistic electrons in classical regime, such as astrophysics, high-energy laser-plasma systems and so on. As an example, the spin induced ponderomotive force in the interaction of strong EM wave and magnetized plasma is investigated. Results show that the time component of four-spin, which approaches to zero in nonrelativistic situations, can increase the spin-ponderomotive force obviously in relativistic situation.