The boundary element methodology is applied to the fracture mechanics of non-linear viscoelastic solids. The adopted non-linear model is based on the ‘free volume’ concept, which is introduced into the relaxation moduli entering the linear viscoelastic relations through a time shift depending on the volumetric strain. Nonlinearity generates an irreducible domain integral into the original boundary integral equation governing the behaviour of linear viscoelastic solids. This necessitates the evaluation of domain strains, which relies on a non-standard differentiation of an integral with a strong kernel singularity. A time domain formulation based on constant shape functions over boundary elements and domain cells is computer-implemented through a numerical integration algorithm. The effectiveness of the developed numerical tool is demonstrated through the analysis of a plate with a central crack. The predicted stress field around the crack tip is compared with respective results obtained by the finite element method.