A theoretical model of the EOF and hydrodynamic flow in wide closed cylindrical capillaries, after the application of a stepwise voltage, is developed. Analytical expressions have been obtained as a sum of the solutions for the direct flow and backflow in both periodical and aperiodical regimes with arbitrary pulse/pulse or pulse/pause durations and amplitudes. The numerical analysis, performed for a few types of periodical and aperiodical regimes, shows the qualitative peculiarities of the liquid velocity profiles and its displacement for different numbers of pulses. The obtained results are compared with those obtained in the case of open capillaries. The possibility of the application of aperiodical stepwise regime for the investigation of electrophoresis is discussed.