A simplified elastic hand-method of analysis for asymmetric multi-bent structures with cores subjected to horizontal loading is presented. The structures may consist of combinations of framed structures such as coupled walls, rigid frames and braced frames with planar and non-planar shear walls. Results for structures that are uniform with height compare closely with results from stiffness matrix analyses. The method is developed from coupled-wall deflection theory which is expressed in non-dimensional structural parameters. It accounts for bending deformations in all individual members, axial deformations in the vertical members as well as torsion and warping in nonplanar walls. A closed solution of coupled differential equations for deflection and rotation gives the deflected shape along the height of the building from which all internal forces can be obtained. The proposed method of analysis offers a relatively simple and rapid means of comparing the deformations and internal forces of different stability systems for a proposed tall building in the preliminary stages of the design. The derivation of equations for analysis shown in this paper are for unisymmetric stability systems only, but the method is also applicable to general asymmetric structures with cores. Copyright © 2002 John Wiley & Sons, Ltd.