It is hardly possible to make experiments on transport of potentially dangerous tracers in a sea. Therefore numerical simulation is successfully used to assess the risks and consequences of various events like oil spills, flux of toxicants with river runoff after industrial accidents or phytoplankton in case of harmful algae bloom. As the White Sea is a transport hub and a strategically important location for extraction of natural resources, so it is important to know the most likely scenarios of pollutants behavior. The JASMINE numerical model, based on the FEMAO (Finite-Element Model of the Arctic Ocean) simulates evolution of sea state, including three-dimensional currents, temperature and salinity, and sea ice, and is able to calculate tracer advection, so giving answers to a number of questions related to how pollution evolves in the White Sea. We describe numerical experiments to study advection of floating tracers in the White Sea when the initial distribution is delta-like and located in the mouths of main rivers. Also, we calculate the time of almost complete removal of an initially homogeneous concentration of a passive tracer. Spatial resolution is 3 km, vertical grid is 5 m down to the depth level of 150 m (10 m for depths more than 150 m). The time step is 360 s. NOAA/NCEP atmospheric reanalysis is used for atmospheric forcing. Five main rivers are taken into account with the monthly-mean runoff taken from the multi-year observation data. We have estimated the time needed to remove most of the matter from the sea; it depends on morphometric characteristics of the bays and is the highest for the Onezhskiy bay. Matter exchange between the bays is low, only Dvinskiy-Onezhskiy-Mezenskiy transport is present, as we would expect from the geostrophic current pattern.