The short-living cosmogenic isotope 7Be, which is produced by cosmic rays in the atmosphere, is often used as a tracer for atmospheric dynamics, with precise and high-resolution measurements covering the recent decades. The long-living isotope 10Be, as measured in polar ice cores with an annual resolution, is a proxy for long-term cosmic-ray variability, whose signal can, however, be distorted by atmospheric transport and deposition that need to be properly modeled to be accounted for. While transport of 7Be can be modeled with high accuracy using the known meteorological fields, atmospheric transport of 10Be was typically modeled using case-study-specific simulations or simplified box models based on parameterizations. Thus, there is a need for a realistic model able to simulate atmospheric transport and deposition of beryllium with a focus on polar regions and (inter)annual timescales that is potentially able to operate in a self-consistent mode without the prescribed meteorology. Since measurements of 10Be are extremely laborious and hence scarce, it is difficult to compare model results directly with measurement data. On the other hand, the two beryllium isotopes are believed to have similar transport and deposition properties, being different only in production and lifetime, and thus the results of 7Be transport can be generally applied to 10Be. Here we present a new model, called CCM SOCOL-AERv2-BE, to trace isotopes of 7Be and 10Be in the atmosphere based on the chemistry-climate model (CCM) SOCOL (SOlar Climate Ozone Links), which has been improved by including modules for the production, deposition, and transport of 7Be and 10Be. Production of the isotopes was modeled for both galactic and solar cosmic rays by applying the CRAC (Cosmic Ray Atmospheric Cascade) model. Transport of 7Be was modeled without additional gravitational settling due to the submicron size of the background aerosol particles. An interactive deposition scheme was applied including both wet and dry deposition. Modeling was performed using a full nudging to the meteorological fields for the period of 2002-2008 with a spin-up period of 1996-2001. The modeled concentrations of 7Be in near-ground air were compared with the measured ones at a weekly time resolution in four nearly antipodal high-latitude locations: two in the Northern (Finland and Canada) and two in the Southern (Chile and the Kerguelen Islands) Hemisphere. The model results agree with the measurements in the absolute level within error bars, implying that the production, decay, and lateral deposition are correctly reproduced. The model also correctly reproduces the temporal variability of 7Be concentrations on annual and sub-annual scales, including the presence and absence of the annual cycle in the Northern and Southern Hemisphere, respectively. We also modeled the production and transport of 7Be for a major solar energetic particle event (SPE) on 20 January 2005, which appears insufficient to produce a measurable signal but may serve as a reference event for historically known extreme SPEs. Thus, a new full 3D time-dependent model, based on CCM SOCOL, of 7Be and 10Be atmospheric production, transport, and deposition has been developed. Comparison with real data on the 7Be concentration in the near-ground air validates the model and its accuracy.