In the paper a rigorous continuous media theory with conserved dislocations is developed and the variant of continuous theory of the adhesion interactions is proposed. The adhesion interactions for the defectless media, for the media with dislocation field in the volume and on the surface are introduced. We used “kinematic” variational approach to constructing models of continuous media with a generalized kinematics. . The important feature of the newly developed classification is a new kinematic interpretation of dislocations, which reflects the connection of dislocations with free rotation, free change of volume (porosity) and free forming for a 3D, 2D and 1D considerations. On the basis of the variational kinematic principle the set of constitutive relations is derived and the corresponding consistent boundary-value problems are formulated. The potential energy in the volume and on the surfaces are considered and definitions for the supermodules, “damage” and “loosening” states are` given in 3D and 2D. The integral Clapeyron type’s theorems for the media with conserved dislocations and the Griffith’s theorem for the stability of the cracks are established.