An analysis is presented of the kinematic consequences and dynamical causes of paleomagnetically determined rotations about a vertical axis, documented in the central Andes, South America, between 15¿S and 25¿S. At these latitudes, there is a pronounced bend in the topographic and structural trends, defining the Bolivian orocline. The observed vertical axis rotations during the last 10 Myr are used, in conjunction with observations of horizontal dilatation, to calculate the finite strain and displacement field in a network of triangles spanning the Bolivian orocline, assuming that the rotations represent the rotational component of finite strain. This shows that rotation during the last 10 Myr has accommodated bending of the Bolivian Andes, increasing the curvature of the eastern margin of the Bolivian orocline by 10¿ to 27¿, with a systematic variation in strains around the oroclinal hinge which is consistent with the observed pattern of upper Miocene to recent deformation. Vertical axis rotations, greater than that inferred for regional oroclinal bending, can be explained in terms of simple kinematic models of vertical axis rotation and reverse faulting in margin-parallel zones of sinistral and dextral shear. The dynamical controls of vertical axis rotation are analyzed using a simple thin sheet model of viscous flow in a narrow channel. This model suggests that, in general, regional bending is controlled by a combination of along-strike gradients of (1) boundary normal stresses at the subduction zone; (2) bulk lithospheric viscosity; (3) gravitational potential energy (buoyancy stress) contrasts; and (4) width of the fluid-like channel. If along-strike gradients of boundary normal stresses and viscosity are small, then the pattern of vertical axis rotation can be explained as a consequence of along-strike gradients in buoyancy stress for a bulk lithospheric viscosity in the Bolivian Andes >7¿1021 Pa s. In detail, the organization of vertical axis rotation and horizontal shortening suggests that there are both horizontal and vertical gradients of velocity and rheology in the lithosphere. ¿ 2001 American Geophysical Union