To determine the artificial fracture initiation point is located in the distal radial well natural cracks or near wellbore zone for the purpose of study, based on mass and momentum conservation, considering the viscosity and the compressibility of liquid, a power-law pad fluid pressure wave transmitting mathematical models is developed. The pressure wave velocity is calculated by Finite Difference Method and verified by experiments. Compared experimental result to computing result,the average calculation error is 4.70% and the mathematical model of pressure wave propagation shows higher accuracy. On this basis, a function about horizontal well pressure distribution and pressure velocity is derived. Through the research of pressure transfer law of power-law pad fluid in horizontal wells, the pressure distribution of horizontal wells especially radial horizontal wells could be revealed and a theoretical basis for the fine description of the pad fluid pressure distribution can be provided.