A certain type of alloys, with face-centered-cubic (FCC) structure and medium to low stacking fault energies (SFE), can trigger the formation of multiple twins (mechanical twinning), along with dislocation glide, when deformed, providing an exceptional strength-ductility combination at both room and cryogenic temperatures. Further understanding of mechanical twinning behavior will aid the design and development of new alloys. In this study, we aim to probe the tension-compression asymmetry upon cyclic loading at cryogenic temperatures of FCC alloys with low SFE (a high entropy alloy and a twin induced plasticity steel), in order to reveal the origin of the pronounced Bauschinger effect and the feasibility of de-twinning in this alloy system.