FCNC processes offer important tools to test the Standard Model (SM) and to search for possible new physics. In this work, we investigate the rare hyperon decays in SM and beyond. We find that in SM the branching ratios for these rare hyperon decays range from to . When all the errors in the form factors are included, we find that the final branching ratios for most decay modes have an uncertainty of about 5% to 10%. After taking into account the contribution from new physics, the generalized SUSY extension of SM and the minimal 331 model, the decay widths for these channels can be enhanced by a factor of .