In order to solve the problem of selecting prepress printing parameters (printing speed, printing pressure, etc.), a series solution of ink penetration pressure distribution was proposed. Considering the change of paper compression, the series solution of the time-space evolution of ink penetration pressure distribution in paper was derived using one-dimensional seepage equation; based on the numerical solution and experimental data, the numerical experiment of ink penetration pressure distribution in printing process was carried out, and the time-space evolution equation of ink penetration pressure distribution based on experimental parameters was established. The time-space evolution curve of ink penetration pressure distribution in compressible paper was drawn, and the time-space evolution simulation of printing pressure distribution was realized. This paper presents a series analytical method of ink penetration pressure in compressible paper, which can realize the quantitative analytical calculation and simulation of the spatial and temporal evolution of ink penetration pressure distribution, and provide a theoretical basis for the selection and design of prepress printing parameters.