Abstract <p> In the paper, functional identities for the difference between a given function and theexact solution of the generalized Stokes problem are derived. The restrictions on the form of sucha function are minimal. Actually, they are reduced to the requirement that it must belong to thesame function class as the solution of the problem. The left part of the identity represents aweighted sum of norms and characterizes deviations from the exact velocity and stresses fields.The right part includes a number of terms. Some of them can be directly computed from theproblem data and known approximate solutions. Other terms contain unknown functions but canbe efficiently estimated. Hence the identity is a basis for getting fully computable two-sidedbounds for the distance to the solution of the problem. The identities and the estimates derivedfrom them can be used to estimate errors of approximations generated by various numericalmethods. They are true both for solenoidal approximations as well as for those that satisfy theincompressibility condition only with a certain degree of accuracy. In addition, these identitiesand estimates permit one to compare exact solutions of problems with different data. Therefore,they open a way to evaluate errors of mathematical models, e.g., those that arise after changing(simplification) of the differential equation or due to replacing the incompressibility condition byweaker conditions.</p>