A method to evaluate the static response bounds of structures with uncertain parameters modelled as interval variables is proposed. The method is very suitable when the data are insufficient for a probabilistic model of the uncertainties and overcomes the drawbacks arising in traditional interval analysis due to dependency phenomenon. The procedure is based on the inversion of the interval stiffness matrix by means of a novel approximate relationship built on the interval-valued Sherman-Morrison-Woodbury formula. Numerical results evidence the accuracy and the effectiveness of the proposed approach in the evaluation of the response bounds. © 2011 Taylor & Francis Group, London.