The work aims to clearly and intuitively understand the microscopic mechanism of the process of spreading the electronic ink of the gravure printing. According to the ink spreading process, the static physical and geometric models were established. The power law fluid theory was used to analyze the relationship between ink viscosity and shear rate, especially the power law fluid function model of nano silver conductive ink. Finally, the experiment was used to verify the correctness of such model. The power law fluid theory showed that the viscosity and the shear rate of nano silver conductive ink was subject to a numerical relationship . The experimental results showed that, when the printing pressure was 49 N, the line width expansion rate was the largest and the printing speed was 21.88 mm/s, the sheet resistance under such condition was verified to be 5.915 Ω; when the printing speed was 45 mm/s, the line width expansion rate was the largest and the printing pressure was 49.36 N, the sheet resistance under such condition was verified to be 5.908 Ω. When the printing pressure was 49 N, the printing speed was 45 mm/s, the line width expansion rate was the largest and the ink viscosity was 0.78 Pa•s, the sheet resistance under such condition was verified to be 4.8998 Ω. There was a functional relationship between ink viscosity η and printing speed v. Nano silver conductive ink is a pseudo plastic fluid with a negative correlation between viscosity and shear rate. The shear rate is a key parameter affecting the ink spreading process.