This work presents a description of the stress-strain state of a crack in an elastic material based on the consideration of non-local interactions between continuum particles. A flat crack in a state of equilibrium is examined. The edges of the crack gradually come together at its corners, having a common tangent plane. In the classical model, this results in infinite stresses. The Barenblatt model indicates finite stresses due to non-local interactions between the crack edges. The elastic medium model used in the description confirms this. It is assumed that the crack arose as a result of the delamination of a homogeneous isotropic elastic continuum under the influence of internal stresses that are perpendicular to it. These stresses are believed to be due to internal forces that exist in the material in the absence of external forces. In the model used, it is considered that each particle can interact with any other particle and pairs of particles through potential forces. The non-local model can be transformed into a gradient model, in which the kinematics of the continuum is described not by one, but by multiple gradients of displacements of increasing rank. This transformation is based on the expansion of the relative positions of the material particles into a series according to their relative positions in the reference configuration. The non-local model employed reflects the truly existing non-local intermolecular interactions, including those between the edges of the crack, which the Barenblatt model suggests to take into account. The parameters of the potentials are expressed in terms of Young’s modulus, shear modulus, and the curvature of the dispersion law graph. The work demonstrates that the edges of the crack can be considered as material surfaces with their own material characteristics and as elastic beams of finite thickness. As an example, the model of the surface layer—a beam—is used to assess the degree of crack opening in an elastic material under natural conditions. It is shown that this opening has a small but finite magnitude. The study indicates that the considered model of non-local interactions between continuum particles allows for both qualitative and quantitative assessment of the impact of a specific property of metamaterial—the negative Poisson’s ratio on the calculation results.