In the previous publications we have proposed a general algorithm for constructing the Lagrange functionals. This general algorithm is based on the analysis of kinematic links that are intrinsic properties of a holonomic medium under consideration. In the presented paper, we extend this kinematic approach to the construction of a model of nonholonomic media. The kinematic variational approach differs from the variational approach proposed by L.I.Sedov such that the list of arguments in corresponding functionals are depend strictly on the choice of kinematic links. We obtain the general form of governing equations for nonholonomic media. These equations are the conditions of non-integrability of virtual work of inner stress parameters. We obtain the variational equation for nonholonomic linear media and state the corresponding boundary value problem (initial and boundary value problem).