A theoretical description is given for a single-electron charging of cylindrical quantum dots. This work is motivated by the recent capacitance-spectroscopy experiments with self assembled InAs quantum dots. We have applied the unrestricted Hartree-Fock method to calculate the energy levels of artificial-atom states with N = 1-8 electrons in a three-dimensional disk-shaped potential well of finite depth. We have calculated the magnetic-field dependence of chemical potentials for N electrons in the dot and determined the positions of capacitance peaks as functions of the applied magnetic and electric fields. The numerical results very well agree with experimental data. We have also considered the influence of the geometry of the device on the spin-orbital configuration of the occupied states and discussed an applicability of two-dimensional model for electrons in cylindrical quantum dots.