Scanning electrical impedance imaging (SII) is a previously-introduced high resolution imaging modality with the potential of imaging the electrical activities of biological tissues. In this paper, a detailed complex electrostatic model is derived to describe the physical phenomena of the SII system. This model reveals the relationship between the voltage measurement and impedance distribution and also shows how system parameters such as height affect the resolution of the impedance image. A numerical solution is developed for this model based on the finite difference method (FDM). A variation of classical FDM is used to solve the complicated boundary conditions introduced by the combination of the electrostatic field and the peripheral circuit. Good correspondence can be observed when comparing the model simulation with experimental data acquired during a line-scan. It can be seen that the model provides a good explanation for the experimental results and can assist in the design of the special dual-conductor impedance probe used in the SII system. A two-source improvement for the SII system which is motivated by the modelling work is implemented and the corresponding physical analysis is obtained. It can help the reduction of the current contribution from the shield to the tip so that higher resolution can be achieved.