The problem of recovering the plasticity function of non-linear Lame equation from the knowledge of penetration diagram is considered. Mathematical modelling of the identification problem leads to an inverse Signorini problem for a non-linear operator with a non-local additional condition (measured data). Using a variational method coefficient stability in H-1 is proved. Then based on this result, the existence of a quasisolution is obtained in a physically admissible class of coefficients. The numerical method and examples are also presented. (C) 1998 Elsevier Science Ltd. All rights reserved.