Continuum models were constructed to describe large‐scale deformation of the Aleutian Island Arc over the past 5 m.y. These models consider the island arc as a continuum in the horizontal plane with the velocity boundary condition at the Pacific edge stated as a fraction of Pacific plate convergence transferred to the arc. First, a simple model of uniformly distributed strain is formulated to illustrate the mechanics of continuous deformation. Lineaments along the arc massif rotated about a vertical axis are matched by small‐element rotation calculated from the model. However, this model does not predict across‐arc variations in deformation and produces an unrealistic amount of crustal thickening after 5 m.y. A physically more meaningful model of deformation is the thin viscous sheet model based on averages of stress and rheology throughout the lithosphere. The amount of motion transferred from the Pacific plate to the arc is constrained by the rotated lineaments, while the effective stress‐strain exponent (n) and the ability the lithosphere has to sustain crustal thickness contrasts (the Argand number) are independent variables. Primarily, bathymetry, earthquake focal mechanisms, and styles of faulting are used to evaluate the models. The preferred model is one where the amount of motion transferred from the Pacific plate is greater in an arc‐parallel direction than in an arc‐normal direction, producing stresses consistent with strike‐slip faulting at the far western end of the arc and tensional stresses consistent with transverse normal faulting elsewhere in the arc massif. This model agrees with observations of slip vectors by Ekström and Engdahl (1989), who conclude that a portion of the arc‐parallel component of relative plate motion is taken up in the overriding plate. This model implies that compressive stress transferred to the arc is small in comparison to along‐arc shear stress and that stresses conducive to strikeslip faulting are prevalent throughout the arc.