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Entropic property of the Ellipsoidal Statistical model with the Prandtlnumber Pr below 2/3 is discussed. Although 2/3 is the lower bound of Pr for theH theorem to hold unconditionally, it is shown that the theorem still holdseven for $\mathrm{Pr}<2/3$, provided that anisotropy of stress tensor satisfiesa certain criterion. The practical tolerance of that criterion is assessednumerically by the strong normal shock wave and the Couette flow problems. Acouple of moving plate tests are also conducted.

On the entropic property of the Ellipsoidal Statistical model with the Prandtl number below 2/3