In this paper, we present the model of continuum mechanics for an analysis of the size-dependent elastic state of the wrinkled thin film coating with the nanosized thickness. For this purpose, we formulate the two-dimensional boundary value problem for the film-on-substrate system under plane strain conditions in terms of the complex variable. To analyse the effect of surface and interface elasticity, the surface and interphase domains are modelled as negligibly thin layers adhering to the bulk phases without slipping. The algorithm of deriving the expressions for the stress tensor components in the first-order approximation of the boundary perturbation method is described. Based on this algorithm, the influence of the size of the wrinkles, film-to-substrate stiffness ratio and film thickness on the stress concentration in the film is examined.