In electroencephalography (EEG) source analysis, a primary current density generated by the neural activity of the brain is reconstructed from external electrode voltage measurements. This paper focuses on accurate and effective simulations of EEG through the complete electrode model (CEM). The CEM allows for the incorporation of the electrode size, shape and effective contact impedance into the forward simulation. Both neural currents in the brain and shunting currents between the electrodes and the skin can affect the measured voltages in the CEM. The goal of this study was to investigate the CEM by comparing it with the point electrode model (PEM), which is the current standard electrode model for EEG. We used a three-dimensional, realistic and high-resolution finite element head model as the reference computational domain in the comparison. The PEM could be formulated as a limit of the CEM, in which the effective impedance of each electrode goes to infinity and the size tends to zero. Numerical results concerning the forward and inverse errors and electrode voltage strengths with different impedances and electrode sizes are presented. Based on the results obtained, limits for extremely high and low impedance values of the shunting currents are suggested.