The sheath criterion was considered for electronegative as well as electropositive plasma in contact with a material boundary that is either more negative than the plasma space potential or more positive than the space potential. A fluid model accounted for the inertia and pressures of all the plasma components and the Sagdeev potential in the whole sheath without any power series expansion were used. The criterion was specified for several special cases of both electronegative and electropositive plasmas. In the cases, a cold ion critical velocity at the sheath entrance was greater by a factor of 1.585 for qφ>0 than that for qφ<0, where q is the ion charge and φ is the electrical potential in the sheath. In the case of a plasma with Boltzmann electrons and positive ions and a cold ion beam, this conclusion is true only for q < 0 and φ< 0.
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