In this paper we discuss the constitutive relations for micropolar plates recently obtained by Altenbach and Eremeyev. We pay particular attention to their relation for the resultant drilling stress couple and compare it with that used so far in the statically and kinematically exact nonlinear six‐parameter shell theory. Using the results of Altenbach and Eremeyev, we present bounds on values of the constitutive parameter αt from the six‐parameter shell theory model. Some representative numerical simulations show how the drilling stiffness αt affects the FEM results.