The detonation process was studied theoretically and experimentally for circularly curved charges with both square and circular cross sections. Velocities of the front of the detonation wave along the inner and outer edge were monitored. For comparison with numerical simulations, the results of experiments from Lawrence Livermore National Laboratory (LLNL), USA and Department of Theory and Technology of Explosives (DTTX), Czech Republic were used. The ribs were simulated with LS-DYNA code utilizing beta burn model for the explosives. The results of the numerical simulations were in a very good agreement with the experimental data.