The stable carbon isotopic composition ([delta].sup.13 C) is an important variable to study the ocean carbon cycle across different timescales. We include a new representation of the stable carbon isotope .sup.13 C into the HAMburg Ocean Carbon Cycle model (HAMOCC), the ocean biogeochemical component of the Max Planck Institute Earth System Model (MPI-ESM). .sup.13 C is explicitly resolved for all oceanic carbon pools considered. We account for fractionation during air-sea gas exchange and for biological fractionation Ïµ.sub.p associated with photosynthetic carbon fixation during phytoplankton growth. We examine two Ïµ.sub.p parameterisations of different complexity: ÏµpPopp varies with surface dissolved CO.sub.2 concentration (Popp et al., 1989), while ÏµpLaws additionally depends on local phytoplankton growth rates (Laws et al., 1995). When compared to observations of [delta].sup.13 C of dissolved inorganic carbon (DIC), both parameterisations yield similar performance. However, with regard to [delta].sup.13 C in particulate organic carbon (POC) ÏµpPopp shows a considerably improved performance compared to ÏµpLaws. This is because ÏµpLaws produces too strong a preference for .sup.12 C, resulting in [delta].sup.13 C.sub.POC that is too low in our model. The model also well reproduces the global oceanic anthropogenic CO.sub.2 sink and the oceanic .sup.13 C Suess effect, i.e. the intrusion and distribution of the isotopically light anthropogenic CO.sub.2 in the ocean. The satisfactory model performance of the present-day oceanic [delta].sup.13 C distribution using ÏµpPopp and of the anthropogenic CO.sub.2 uptake allows us to further investigate the potential sources of uncertainty of the Eide et al. (2017a) approach for estimating the oceanic .sup.13 C Suess effect. Eide et al. (2017a) derived the first global oceanic .sup.13 C Suess effect estimate based on observations. They have noted a potential underestimation, but their approach does not provide any insight about the cause. By applying the Eide et al. (2017a) approach to the model data we are able to investigate in detail potential sources of underestimation of the .sup.13 C Suess effect. Based on our model we find underestimations of the .sup.13 C Suess effect at 200 m by 0.24 0/00 in the Indian Ocean, 0.21 0/00 in the North Pacific, 0.26 0/00 in the South Pacific, 0.1 0/00 in the North Atlantic and 0.14 0/00 in the South Atlantic. We attribute the major sources of underestimation to two assumptions in the Eide et al. (2017a) approach: the spatially uniform preformed component of [delta].sup.13 C.sub.DIC in year 1940 and the neglect of processes that are not directly linked to the oceanic uptake and transport of chlorofluorocarbon-12 (CFC-12) such as the decrease in [delta].sup.13 C.sub.POC over the industrial period. The new .sup.13 C module in the ocean biogeochemical component of MPI-ESM shows satisfying performance. It is a useful tool to study the ocean carbon sink under the anthropogenic influences, and it will be applied to investigating variations of ocean carbon cycle in the past.