This paper is devoted to the determination of an unknown function that describes elastoplastic properties of a bar under torsion. The mathematical (evolution) model leads to an inverse problem that consists of determining the unknown coefficient g = g(xi(2)), xi(2) = vertical bar del u vertical bar(2), in the nonlinear parabolic equation u(t) - del, (g(vertical bar del u vertical bar(2))del u) = 2t, (x,y,t) epsilon del(t)* := del x(0,t*], del subset of R-2 using measured output data given in the integral form. Existence of a quasi-solution of the considered inverse problem is obtained in the appropriate class of admissible coefficients. The direct problem is solved using a semi-implicit finite difference scheme. The inverse problem is solved using the semi-analytic inversion method (also known the fast algorithm). Finally, some examples are presented related to direct and inverse problems.