Abstract: Two- and one-dimensional Kirchhoff models of thin isotropic plates and rods are combinedinto a single problem describing the deformation of the joint of these elastic objects. Theconjugation conditions at the points of attachment of the rods to the plate are assigned using thetechnique of self-adjoint extensions of fourth-order differential operators in a two-dimensionaldomain and second-order differential operators on one-dimensional segments. Statements ofproblems containing nonlinear transmission conditions, in particular, unilateral constraints, aregiven.