A modified Taylor model, hereafter referred to as the MTCS (Mechanical-Twinning-with-Coplanar-Slip)-model, is proposed in the present work to predict weak texture components in the shear bands of brass-type fcc metals with a twin–matrix lamellar (TML) structure. The MTCS-model considers two boundary conditions (i.e., twinning does not occur in previously twinned areas and coplanar slip occurs in the TML region) to simulate the rolling texture of Cu–30%Zn. In the first approximation, texture simulation using the MTCS-model revealed brass-type textures, including Y{1 1 1} and Z{1 1 1} components, which correspond to the observed experimental textures. Single orientations of C(1 1 2)[1¯ 1¯ 1] and S’(1 2 3)[4¯ 1¯ 2] were applied to the MTCS-model to understand the evolution of Y and Z components. For the Y orientation, the C orientation rotates toward T(5 5 2)[1 1 5] by twinning after 30% reduction and then toward Y(1 1 1)[1 1 2] by coplanar slip after over 30% reduction. For the Z orientation, the S’ orientation rotates toward T’(3 2 1)[2 1¯ 4¯] by twinning after 30% reduction and then toward Z(1 1 1)[1 0 1¯] by coplanar slip after over 30% reduction.