Some alkali and alkaline earth metals can now be encapsulated in fullerenes. For example, Li@C60 and Li@C70 can be produced by the low energy bombardment method while Ca@C74, Sr@C74 and Ba@C74 can be prepared by high temprature synthesis. Hence, their computations at higher levels of theory are also of interest. In the report, the computations are carried out on Li@C60, Li2@;C60 and Li3@;C60 with the B3LYP and MPWBIK density-functional theory (DFT) treatment in the standard 3-21G and 6-31G* basis sets. The computed energetics suggests that Lix@;C60 species could be produced at several small x values if the Li pressure is enhanced sufficiently. The B3LYP DFT approach is also applied to Mg@C74, Ca@C74, Sr@C74 and Ba@C74 and production populations are thus rationalized.