It is proposed that the Li abundances in F-type stars can be affected by the weak mixing generated by internal gravity waves since the absence of Li is so strong among this spectral type. The mixing mechanism caused by the waves is describe theoretically and is applied to the F-stars because of the inherent similarity of the Li gap. The wave-energy flux is found to grow with age, the flux values of the Li and Be burning layers are similar, and the resulting predictions for young stellar systems are compatible with observational data.