Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.