The principle of the minimum shear amount was applied for rolling texture formation of fcc metal. The model is based on an assumption that from the three equivalent shear groups indivisually composed of eight <110> shear systems on the four {111} planes around the principal axes X[100], Y[010] and Z[001],only one group in the shear systems, may operate under the minimum shear magnitude principle. Firstly, one model on the full constraints condition, considering the twelve shear systems of fcc metal as a whole,which was combined Taylor's theory of the essential five shears with none shear plane, reproduced Taylor({4411}<11118>) (remarkably) and Brass({110}<112>) increasingly with cold reduction. The results were different according to selection of the specified {111} plane assigned for the none shear plane. It was also shown that rolling texture changed in the simulation in such way from S1({123}<634>)-->S2({124}<211>)-->S3({124}<865>)-->S4({237} <654>)-->Taylor with cold reduction. Secondly,another model where specified one of the four {111} is either always perfectly (= no zero slip component) or always imperfectly(= at least one zero slip component) activated during cold rolling,presumably simulating fcc metal with fault, reproduced mainly Brass and S5({237}<211>) increasingly with cold reduction whereas it depressed Taylor and S4. In both simulations,selection of the specified plane showed singular inclination in the rolling texture and selection of (1 (1) over bar1)("2") and ((1) over bar 11)("4") gave same texture due to geometrical symmetry. The results showed how the fcc texture formation changes with selection of the none shear plane from the four {111} in Taylor's five shear model and does with selection of perfectly or imperfectly activated plane from the four as well,even suggesting how pure metal type is generated by Taylor's essential five shears and alloy type by heterogeneity of slip such that one or two specified from the four {111} planes is always either perfectly or imperfectly activated.