Electric fields can be used to change and control flame properties, for example changing flame speed, enhancing flame stability, or reducing pollutant emission. The ions generated in flames are believed to play the primary role. Although experiments have been carried out to study electric field enhanced combustion, they are not sufficient to explain how the ions in a flame are affected by an electric field. It is therefore necessary to investigate the problem through numerical simulations. In the present work, the electric structure of stabilized CH4/air premixed flames at atmospheric pressure within a direct current field is studied using numerical simulations. This study consists of three parts. First, the transport equations are derived from the Boltzmann kinetic equation for each individual species. Second, a general method for computing the diffusivity and mobility of ions in a gas mixture is introduced. Third, the mechanisms for neutral and charged species are improved to give better predictions of the concentrations of charged species, based on experimental data. Following from this, comprehensive numerical results are presented, including the concentrations and fluxes of charged species, the distributions of the electric field and electric potential, and the electric current-voltage relation. Two new concepts introduced with the numerical results are the plasma sheath and dead zone in the premixed flame. A reactive plasma sheath and a Boltzmann relation sheath are discovered in the region near the electrodes. The plasma sheath penetrates into the flame gas when a voltage is applied, and penetrating further if the voltage is higher. The zone outside the region of sheath penetration is defined as the dead zone. With the two concepts, analytical solutions for the electric field, electric potential and current-voltage curve are derived. The solutions directly describe the electric structure of a premixed flame subject to a DC field. These analytical solutions, together with the discovery of the plasma sheath and dead zone in flames, are the novel contributions of this work.