The purpose of this work is to analyse the behaviour of steels of Low Yield Point (LYP), applying mechanical cyclic loads. To define the cyclic behaviour and obtain the behaviour of resistance, ductility and energy dissipation, numerical simulations were carried out of two structural steels (LYP100 and LYP160) and a conventional steel (Q235B), applying monotonic and cyclic loading patterns, using the analytical model by nonlinear kinematic hardening for Mróz-Garud stress fields. The results obtained in this study show consistency with recent publications, revealing that, despite the low elastic limit of the LYP steels, they improve their cyclic, ductile and energy dissipation responses, important for the control of the seismic response.