Thin plates find applications in several scientific and technical fields. We recall here the case of plate elements for a bridge deck. In certain situations, it may be mandatory to ensure the embedding and support of these plates for correct installation of this structure. However, direct measurements may be impossible or difficult to obtain during construction or during maintenance. An opposite problem then arises! Objectives: The aim of this study is to solve the inverse Cauchy-type problem for the bilaplacian operator, which governs the bending of thin plates, such that the boundary conditions are only available on part of the boundary. We propose to apply the fading regularization method and implement it numerically using discrete Kirchhoff (DK) plate elements.