We consider the steady, slow translational fall of a rigid body B in a second-order fluid, under the action of the acceleration of gravity g. We find a general expression for the total force and torque acting on B. In particular, the force per unit area is always compressive, if the first normal stress coefficient Psi (1) is positive. We then specialize these formulas to the case when B is a prolate spheroid of eccentricity e, and show that, when 0 < e < 1, there are only two orientations of fall allowed, namely, when the major axis of B is either perpendicular or parallel to g. However, we show that if Psi (1) > 0, only this latter orientation is stable to small disorientations, in agreement with the recent experimental results of Joseph and coworkers.