As a sequel to an earlier study of asymptotic theory of thin hyperlastic plates, the special case of incompressible plates is presented. The incompressibility condition is used to eliminate the arbitrary pressure function. It is shown that the results obtained in Part I are also valid for the incompressible solid under a transformation of coefficients in the constitutive equations. To illustrate the application of the general theory to a simple problem prone to an analytical treatment, an infinitely long strip under uniform load for various edge conditions is investigated. In the special cases of Ko, Mooney-Rivlin and Neo-Hookean solids, the results are compared with the solutions based upon the geometric nonlinearity.