AbstractAlthough snow plays an important role in the energy and mass balance of sea ice, it is little studied in the Southern Ocean. We present a Lagrangian model of snow on sea ice, CASSIS, that simulates the daily creation and drift of floes. Drifting floes accumulate snow from the atmosphere and the Antarctic ice sheet, and lose snow to the ocean and snow‐ice formation. The depth of snow on Southern Ocean sea ice increases in all sectors between autumn and spring 1981–2021, reaching 40 cm in much of the Weddell Sea, coastal Amundsen Sea and south east Indian Ocean. The root mean square difference between seasonally‐averaged model and ship‐based snow depths is 13.1 cm, and between modeled and airborne snow depths from Operation IceBridge is 13.5 cm. Our model offers an alternative long‐term snow depth record to that from passive microwave (PM) radiometry, which does not capture the seasonal growth of the snow cover. We find that although the average circumpolar snow layer thickness has increased by 16 mm between 1981 and 2021 (P = 0.004), there has been a decrease of 13 mm in the Southern Pacific Ocean (P = 0.133, but significant in spring and autumn), driven by a reduction of summer sea ice extent in this region. Our model paves the way for improved satellite‐based estimates of Antarctic sea ice thickness.