<jats:p>Abstract. Modelling the evolution of the Earth system on long timescales requires the knowledge and understanding of driving mechanisms, such as the hydrological cycle. This is dominant in all components of the Earth's system, such as atmosphere, ocean, land surfaces/vegetation and the cryosphere. Observations and measurements of stable water isotopes in climate archives can help to decipher and reconstruct climate change and its regional variations. For the cryosphere, the δ18O cycle in the current generation of Earth system models is missing and an efficient and accurate tracer transport scheme is required. We describe ISOPOLIS 1.0, a modular semi-Lagrangian transport scheme of second-order accuracy, which is coupled to the polythermal and thermomechanical ice sheet model SICOPOLIS (version 2.9). Model skill is demonstrated by experiments with a simplified ice sheet geometry and by comparisons of simulated ice cores with data from Greenland (GRIP) and Antarctica (Vostok). The presented method is a valuable tool to investigate the transport of any kind of passive tracer inside the cold ice part of a polythermal ice sheet and is an important step to model the whole δ18O cycle. </jats:p>