A definite interest to the studies of deformation of thin and hyperfine films is caused by demand to production of new structural materials and coatings, as well as by wide application of films in the products used in information technologies (semiconductor elements of large-scale integration circuit) and other industries. It is known, however, that using the classical theory of elasticity, it is impossible to describe some aspects of behavior of such films. Particularly, there are not known consistent continual models, which can be used to explain the effect of super modulus discovered in the experiments with thin structures. We make an attempt to derive a variant of linear theory of thin films and use a variant of the theory of continuum derived in an assumption of existence of kinematic connections of general type. These kinematic connections are equivalent to the particular force interactions, the value of which can be defined by a set of corresponding physical constants. Such a model presumes existence of physical constants of different metrical dimension. Part of them describe ordinary elastic properties, the others are related with surface effects and internal interactions similar to the Van der Waals forces of cohesion. It is shown that within the model of media proposed, there exists a principle possibility to describe anomalous increase of stiffness of thin films under their thickness decrease.