The performance of (M, S)-optimality criterion on Regular two-level fractional factorial designs (FFD’s) is studied. The criterion has good estimation capacity and easy to compute. In the past, researchers have used (M, S)-optimality criterion on Regular two-level fractional factorial designs up to two factor interactions (2fi’s). This study is the extension of previous work and (M, S)- optimality criterion is used on Regular two-level FFD’s to two factor interactions (2fi’s) as well as three factor interactions (3fi’s). Models for three factor interactions are used to determine maximum trace Cd and minimum trace 2 Cd for the best designs. New formulae for two factor interactions and three factors interactions are developed and used. Two components of the (M, S) criterion, i.e., trace Cd and trace 2 Cd are derived as explicit functions of the numbers of three- and four-letter words. Generally, (M, S)-optimal designs are not Minimum Aberration MA designs but all MA designs up to 64 runs are (M, S)-optimal. Although main effects, 2fi’s and 3fi’s are focused in this study, but the (M, S) criterion is to be used when 3fis or more than three factors are available.