A technique is developed for analysing elasto-plastic unbounded media by adaptively coupling the finite-element method with the scaled boundary finite-element method. The analysis begins with a finite-element mesh that tightly encloses the load-medium interface, capturing non-linearity in the very near field. The remainder of the problem is modelled accurately and efficiently using the semi-analytical scaled boundary finite-element method. Load increments are applied in the usual (finite-element) way and the plastic stress field grows outwards from the load-medium interface as the solution advances. If plasticity is detected at a Gauss point in the outer band of finite-elements, an additional band of finite-elements are added around the perimeter of the existing mesh and the scaled boundary finite-element domain is stepped out accordingly. This technique exploits the most attractive features of both the finite-element and scaled boundary finite-element methods. The technique is shown to be highly accurate and both user and computationally efficient. (c) 2005 Elsevier Ltd. All rights reserved.