Abstract Tailing and bimodal behaviour of tracer breakthrough curves from tracer tests conducted in fractured porous media are commonly presented as ‘deviations’ from the Fickian model for homogeneous porous media. Tailing is mainly attributed to: (1) tracer storage brought about by diffusion between mobile and static regions of fluid; (2) a concentration of flow towards the wider (aperture) and, thus, more permeable fracture zones; and (3) the high variance in fracture conductivity and consequent mixing of tracer. Bi- (or multi-) modality has been attributed to solute following a few highly permeable flow paths. Systematic numerical simulations of flow and transport in geometrically simple fractured porous media were conducted using a 2D finite difference flow code and a particle tracking transport model. As a simplification only advective dispersion was considered. The modelling study produced a large variety of tracer breakthrough curves, including two patterns commonly seen in field data — the backward tailed uni-modal type and the Gaussian type. The study demonstrates that different types of breakthrough might be characteristic of particular sets of conceptual models for heterogeneities and, as such, may provide a useful pointer in the application and interpretation of tracer tests.