The behaviour of a mechanical structure in the lower frequencies is dominated by constraints at the boundaries. Most structures have elastic supports and specifying the boundary conditions assumes knowledge of the support parameters. In this paper a new method is developed to determine the boundary parameters based on the solution of reduced order characteristic equations. The order of these nonlinear equations is equal to the number of boundary degrees of freedom which is a small fraction of the order of the full structure and means that the amount of computation is not excessive. In this approach no ill-conditioning occurs, which is a common problem other identification procedures. The method is demonstrated by identifying the boundary parameters of a plate on elastic supports by using experimental test data.