The flow properties of dense kaolin suspensions are explored for volume fractions as large as 0.43. The particles were suspended in phosphate buffers at pHs of 7 and 10 where edge‐face interactions are negligible. These platey particles have an aspect ratio of approximately 12 and, thus, are likely to show alignment at volume fractions above a critical volume fraction φ*=0.10. As the concentration is increased from the dilute region of Newtonian behavior, the suspensions develop a yielding type of response near this critical volume fraction. The time dependence of the recoverable strain in some dense suspensions is found to scale on γ̇0twheretis the time after the stress is released and γ̇0is the steady shear rate prior to release of the stress. Over the same time period the elastic modulus remains constant. The magnitude of the modulus is, however, dependent on γ0decreasing from a low shear rate plateau value ofGmax′to a high shear rate plateau value ofGmin′. The shear rate halfway betweenGmax′andGmin′is independent of volume fraction and lies near 0.39D0rotwhereD0rotis the free solution rotational diffusion constant of the plates. This behavior is interpreted as indicating that the plates experience a tumbling/shear aligning transition as the shear rate is raised. Further evidence for alignment is found in shear induced changes in suspension conductivity.