Abstract The method of difference grid construction is used in conjunction with the solution of a physical problem /1/ for solving elastoplastic and gasdynamic problems. Two different variational criteria of coordinate grid selection are considered. The first is based on the investigation of a functional dependent on the flow velocity and motion of moving curvilinear coordinates. An estimate is obtained of the dependence of curvilinear coordinate behavior on the local flow properties. The second criterion is based on the dependence of the functional on the difference scheme variance, and is obtained using the properties of solution of the Hopf equation, as a model. This makes it possible to take into account not only the properties of solution but, also, those of the difference scheme.