In the present study, identification of boundary conditions for elastostatic thin plate bending problems is discussed. In the first step of the research, it is necessary to determine unknown quantities before the identification of the conditions. This paper is concerned with an inverse analysis for the unknown boundary values by the boundary element method (BEM). The unknown boundary values are estimated with additional data for the deflections or the strains given on some internal points of the plate. Some typical numerical calculations show the validity of the present approach, and the usefulness of rank decreasing technique based on singular value decomposition employed with Hansen's L curve method in order to stabilize the numerical solutions on inverse analysis.