The mathematical model leads to the inverse problem of determining the unknown coefficient g = g(xi(2)), xi := vertical bar del u vertical bar, of the non-linear differential equation -del(g(vertical bar del u vertical bar(2))del u)= 2 phi, x is an element of Omega subset of R(2). The inversion method is based on the parametrization of the unknown coefficient, according to the discrete values of the gradient xi := vertical bar del u vertical bar. Within the range of J(2)-deformation theory, it is shown that the considered inverse coefficient problem is an ill-conditioned one. A numerical reconstruction algorithm based on parametrization of the unknown coefficient g =g(xi(2)), with optimal selection of the experimentally given data Tm := T(phi(m)), is proposed as a new regularization scheme for the considered inverse problem. Numerical results with noise free and noisy data illustrate applicability and high accuracy of the proposed method. 2010 Elsevier Ltd. All rights reserved.A new method of determining elastoplastic properties of a beam from an experimentally given value T = T(phi) of torque (or torsional rigidity), during the quasistatic process of torsion, given by the angle of twist phi is an element of [phi(*),phi*], is proposed method. (C) 2010 Elsevier Ltd. All rights reserved.