The work aims to unveil the distribution function law of the printing pressure within offset press to provide a reference basis for the offset press design and the printing quality control. Mooney-Rivlin model was taken as rubber material constitutive model, and the finite element model was established in MSC.Patran to simulate the contact between printing cylinder of offset press and rubber blanket. With MSC.Marc as the solver, the finite element analysis of the model was performed. The finite element analysis was integrated with three nonlinear factors, i.e. nonlinearity of material, geometry and boundary conditions. The contact stress calculations at the finite element nodes were fitted by the least square method. By calculation, the average printing pressure of an offset press was 0.548~0.643 MPa. In the pressing contact area, the distribution function of the normal contact stress on rubber blanket’s outer surface is Gaussian function, and the average printing pressure can be obtained by double integral of Gaussian function.