The various properties for 4-membered ring are studied by semiempirical MINDO/3 calculations. Only 1-2 kcal/mol and 5-7 ckal/mol is required to twist the planar model into the conformations of cephalosporins and penicillins. For the leaving group effect, the $\pi$-electron accepting ability is a major effect and the inductive effect is a minor effect in the substituents in our models. Of the various four membered ring substituents, C$_3$-methoxy group and C$_4$-SH group enhance the amide bond breaking of $\beta$-lactam, but C$_4$-OH group does not. We tried to search the simple theoretical parameters that can be correlated with activities for the various active cephalosporins by semiempirical molecular orbital method, and obtained a mixed result. MM calculations are carried out to obtain model cephalosporin structures, and the resulting geometric variables are in reasonable agreement with the experimental values. In NMDO method, enamine resonance and amide resonance could not be expressed accurately. But in the extreme cases, several parameters correlate with the activity.