Swelling clay suspensions, considered as strongly anisotropic disks, are very unstable in high shear flows. In this study of sodium montmorillonites from Wyoming and China, a hard sphere model is shown to be relevant for the rheological modeling of dilute solutions (2-20 g/L). For more concentrated systems (20-80 g/L), orientation and alignment effects seem to be preponderant. High shear measurements give complete information on the average clay size and critical percolation concentration necessary for the yield stress appearance. At low shear, when interaction effects are dominant, an electrostatic double-layer approach gives directly the average interaction pair potential, allowing good predictions of the elasticity and yield stress of clay dispersions.