A new mixed Eulerian-Lagrangian computational model for simulating and visualizing the internal processes and the variations of dynamic parameters of a two-stage 4K pulse tube cryocooler operating at liquid helium temperature region is developed.The Lagrangian method,a moving grid, is used to follow the exact tracks of gas particles as they move with the pressure oscillation in the pulse tube to avoid any numerical false diffusion.The Eulerian approach,a fixed computational grid,is used to simulate the variations of dynamic parameters in the regenerator.A variety of physical parameters,such as real thermal properties of helium,multi-layered magnetic regenerative materials,pressure drop and heat transfer in the regenerator and heat exchangers,are taken into account. The detailed time-variations of gas temperature,pressure,mass flow rate,enthalpy flow in a cycle,in the first and the second-stage regenerators are presented.Attention is also paid to the effects of different regenerative materials on the performance of the 4K two-stage pulse tube cooler.