Attachment zones couple the rheological layers of lithosphere. In wrench settings, attachment zones accommodate the transition from relatively continuous wrenching at depth to discrete strike-slip faulting of rigid blocks in the upper crust. Strain is controlled by a component of wrench shearing as well as a component of horizontal shearing associated with the differential displacement of finite-width rigid blocks. Strain modelling of wrench attachments predicts high lateral and vertical strain gradients and specific foliation patterns showing antiforms and funnel-shaped synforms. Lineations are shallowly plunging and oriented close to the direction of wrenching. Shear sense reverses across the vertical axial surfaces of synforms and antiforms. In transpression and transtension attachments developed during low-angle oblique convergence or divergence, the pattern of foliation and lineation is similar to that produced in wrench attachments. Transpression attachments display gradients in the shape of the finite strain ellipsoid, from flattening at the base to strongly constrictional beneath the rigid blocks, owing to the increased effect of the horizontal shear component. Conversely, transtension attachments show constriction at the base changing to flattening beneath the rigid blocks. The location of this fabric change within attachment zones is insensitive to finite displacement and angle of convergence or divergence, and therefore should be one of the most robust criteria to identify transpression and transtension attachments. In general, the component of coaxial flow that characterizes transpressional and transtensional systems decreases upward through attachment zones, due to the increased role of the horizontal simple shear in the finite vorticity. These strain and kinematic gradients are a robust result of attachment modelling and can be used as indicators of attachments developed in wrench, transpression, or transtension.