[en] The static-path approximation (SPA) and mean-field approximation (MFA) for the partition function and level density are investigated with the inclusion of spin. The methods are studied within a solvable model, the nuclear SU(3) Elliot model. The SPA partition function is enhanced compared with the MFA partition function and is in good agreement with the exact result at all angular velocities (or spins) and at all but low temperatures. The error made in the SPA as well as in the saddle-point approximation used in the conversion from angular velocity to spin is only weakly dependent on the spin and is small at not too low temperatures (or excitation energies). (orig.)