In the present paper the results of a size effect study on plain concrete unnotched and notched beams loaded in three-point bending are shown and compared with experimental results and Bazant's size effect law. The numerical results, obtained using the nonlocal microplane finite element code, confirm a strong size effect for smaller beam sizes. However, for larger unnotched beams the nominal strength tends to a constant value related to the uniaxial tensile strength. These results are in good agreement with what has been observed in experiments. The reason why the nominal strength of large unnotched beams should approach a limit value different from zero is investigated and the range of applicability of the size effect law is discussed. It has been concluded that the applicability of the size effect law is dependent on the problem type i.e. if the crack propagation before peak load is very stable the size effect law may be used in a rather broad size range. However, if this is not the case, the validity of the size effect law is limited to a smaller size range. Therefore, before extrapolating the size effect from tests with a small size range to a very large size range experimental data from a large size range should be available.