Non-deterministic approaches are gaining momentum in the field of numerical modeling techniques. The ability to include non-deterministic properties is of great value for a design engineer. It enables realistic reliability assessment that incorporates the uncertain aspects of the design. Furthermore, the design can be optimised for robust behaviour under varying external influences. In this context, interval and fuzzy approaches are becoming increasingly popular for the analysis of numerical models that incorporate uncertainty in their description. The interval FEM, which forms the basis of the fuzzy FEM, is based on the interval arithmetic approach or on black-box approaches such as global optimisation. In order to make black-box approaches computationally less expensive, a novel reanalysis-based finite element method (ReFEM) is applied. This paper presents the ReFEM method for static structural analysis. By supplying analytical gradients, this approach is explicitly suited for optimisation-based black-box techniques. The computational benefits and general applicability in the context of fuzzy FE analysis of the new approach is illustrated on a mid-sized plate problem. (C) 2010 Elsevier Ltd. All rights reserved.