The modeling of carbon nanotube ultracapacitor (CNU) performance based on the simulation of electrolyte ion motion between the cathode and the anode is described. Using a molecular dynamics (MD) approach, the equilibrium positions of the electrode charges interacting through the Coulomb potential are determined, which in turn yield the equipotential surface and electric field associated with the capacitor. With an applied ac voltage, the current is computed based on the nanotube and electrolyte particle distribution and interaction, resulting in the frequency-dependent impedance Z(ω). From the current and impedance profiles, the Nyquist and cyclic voltammetry (CV) plots are then extracted. The results of these calculations compare well with existing experimental data. A lumped-element equivalent circuit for the CNU is proposed and the impedance computed from this circuit correlates well with the simulated and measured impedances.