The Mu variant of SARS-CoV-2 has been recently classified as a variant of interest (VOI) by the world health organization (WHO) but limited data are available at the moment.In particular, a special attention was given to the R346K mutation located in the receptor binding domain (RBD).In the current study we performed Free energy of perturbation (FEP) calculations to elucidate it possible impact on a set of neutralizing monoclonal antibodies (mAbs) which have been shown to be strong inhibitors of the most other known COVID-19 variants.Our results show that R346K affects the class 2 antibodies but its effect is not so significant (0.66 kcal/mol); i.e. reduces the binding with RBD about 3 times.An identical value was calculated also in the presence of both class 1 and class 2 antibodies (BD-812/836).Further, a similar reduction in the binding (0.4 kcal/mol) was obtained for BD-821/771 pair of mAbs.For comparison, the addition of K417N mutation, present in the newly registered Mu variant in July 2021 in UK, affected the class 1 mAbs by 1.29 kcal/mol reducing stronger the binding by about 10 times.Thus, the resistance effect of R346K mutation in the Mu variant is possible but not so significant and is due to the addnl. decrease of antibody neutralization based on the reduced binding of class 2 antibodies.