We show that the addition spectra of semiconductor quantum dots in the presence of magnetic field can be studied through a theoretical scheme that allows an accurate and practical treatment of the single-particle states and electron–electron interaction up to large numbers of electrons. The calculated addition spectra exhibit the typical structures of Hund-like shell filling, and account for recent experimental findings. A full three-dimensional description of Coulomb interaction is found to be essential for predicting the conductance characteristics of few-electron semiconductor structures. ©1998 American Institute of Physics.