This technical note examines the shear distortion of plane strain framed structures resulting from tunnelling-induced surface differential settlements. An equation for calculating the shear stiffness is derived, considering various structural parameters. The effectiveness of the proposed method is validated through both experimental and finite element modeling results, with its accuracy emphasized by comparison with existing methods. Additionally, a method for estimating the redistribution of pressure beneath the foundation of plane strain framed buildings due to tunnelling is proposed and validated through numerical simulations which adopt an advanced soil constitutive model. The parametric study further demonstrates the applicability of the proposed methods for estimating shear stiffness in three-dimensional structures characterized by similar vertical wall and horizontal slab stiffness. The research findings provide tunnelling engineers with a tool for the rapid estimation of shear stiffness in framed structures and a reliable evaluation of pressure redistribution beneath foundations caused by tunnelling.