An inverse problem related to the determination of elastoplastic properties of a beam is considered within J2 deformation theory. A new fast algorithm is proposed for the identification of elastoplastic properties of engineering materials. This algorithm is based on finding the three main parameters of the unknown curve g(2) (plasticity function), namely, the elasticity limit [image omitted], the modulus of rigidity G and the strain hardening exponent . The advantage of this algorithm is that only two values of measured output data are required for the reconstruction of the unknown function g(2). Note that all parameterization algorithms use numerous torsional experiments as necessary data for the determination of only some part of the unknown stress-strain curve. Numerical examples related to applicability and high accuracy of the proposed approach are presented for the cases of noise free and noise data.