Summary: We construct the leading terms of asymptotics of solution of the problem of elasticity theory for a thin plate with curved edges; the resulting problem (two-dimensional model) is written out explicitly. Arbitrary anisotropy of elastic properties is allowed; moreover, these properties may depend on ‘rapid’ transversal and ‘slow’ longitudinal variables. The justification of these asymptotics is carried out on the basis of weighted Korn inequality. The cases of laminated plates, shallow shells, and plates with sharp edges are discussed separately.