In this paper, we consider a non-linear viscoelastic model with internal variable, thoroughly analyzed by Le Tallec et al. (Comput. Methods Appl. Mech. Engrg 1993; 109: 233-258). Our aim is to study here the implementation in three dimensions of a generalized version of this model. Computational results will be analyzed to validate our model on toy problems without geometric complexity, for which pseudo-analytical solutions are known. At the end, we present a three-dimensional numerical simulation on a mechanical device. Copyright (C) 2011 John Wiley & Sons, Ltd.