Abstract: In this work, we proposed the electromagnetic model to solve the numerical modelling of the surface wave plasma discharges at atmospheric pressure due to the complexity and vast computing of the common models. According to the discharge characteristics of atmospheric pressure surface-wave plasma, the electromagnetic model was established and simplified reasonably. The results obtained by experimental diagnosis and numerical calculation were compared to verify the reliability of the model and the applicable range of parameters. The effective electron collision frequency obtained by fitting to the experimental data is (1.5±0.25)×10¹¹ s⁻¹, which matches the measured values reported by others. On this foundation, we put emphasis on the influences of plasma density and electromagnetic parameters (electric field distribution and propagation constant) on the external controlling parameters, such as dielectric constant, excitation frequency of 2.45 GHz and 915 MHz, and geometry size of discharge tube (tube thickness and inner radius). The results showed that the electron density and its axial gradient increase with the increasing of the dielectric constant, excitation frequency and tube thickness, but decrease with the tube inner diameter. With regard to the distribution of electric field, the maintenance of plasma is due to the axial component of electric field. As the increase of excitation frequency, the skin depth of surface wave in the media of plasma increases and the radial profile of E_z becomes more uniform. The attenuation and phase constants increase slightly with the dielectric constant and tube thickness, but decrease with the excitation frequency and inner diameter. Simulation results could be used to analyze qualitatively the correlation of the plasma parameters and external controlling parameters.