Abstract. Fission product yields (FY) are fundamental nuclear data for several applications, including decay heat, shielding, dosimetry, burn-up calculations. To be safe and sustainable, modern and future nuclear systems require accurate knowledge on reactor parameters, with reduced margins of uncertainty. Present nuclear data libraries for FY do not provide consistent and complete uncertainty information which are limited, in many cases, to only variances. In the present work we propose a methodology to evaluate covariance matrices for thermal and fast neutron induced fission yields. The semi-empirical models adopted to evaluate the JEFF-3.1.1 FY library have been used in the Generalized Least Square Method available in CONRAD (COde for Nuclear Reaction Analysis and Data assimilation) to generate covariance matrices for several fissioning systems such as the thermal fission of U235, Pu239 and Pu241 and the fast fission of U238, Pu239 and Pu240. The impact of such covariances on nuclear applications has been estimated using deterministic and Monte Carlo uncertainty propagation techniques. We studied the effects on decay heat and reactivity loss uncertainty estimation for simplified test case geometries, such as PWR and SFR pin-cells. The impact on existing nuclear reactors, such as the Jules Horowitz Reactor under construction at CEA-Cadarache, has also been considered.