AbstractA numerical technique is proposed to obtain stress–strain response curves from rate‐type and incremental constitutive equations during generalized loadings. The proposed method linearizes the loading constraints of laboratory experiments, links them to the constitutive relations, and forms a linear system of ordinary differential equations. It circumvents the difficulties associated with the non‐uniqueness and bifurcation of boundary value problems. The method is illustrated for the elastoplastic von Mises and Roscoe and Burland models subjected to torsion, circular stress path, and undrained triaxial compression. The approach pertains to most stress–strain relationships and laboratory experiments of geomechanics. It is useful for research on material modelling, engineering practice and computational me