Abstract: The relative density of non-cohesive soil has a great impact on the engineering properties of soil. For most studies of mesoscopic simulation by using distinct element method (DEM), the first step of the analysis is to create an initial granular assembly with a desired relative density. Based on the DEM, the loosest state is obtained by depositing particles under gravity firstly. Secondly, a quasi vibration and compaction method (QVC) is proposed to simulate the vibration and compaction method by reducing the friction between the particles during the compaction. And the feasibility of QVC method is validated. The densest state is obtained by reducing the friction to zero. The relationship between the friction and packing porosity is studied. Based on this relationship, the friction which is used to obtain the assembly with desired relative density can be estimated. The results show that the relationship between the coordination number of particle and the particle diameter is compatible with an exponential distribution. By reducing the friction between the particles, the vibration process can be well reflected. The relationship between the friction and the packing porosity agrees with the negative exponential distribution. Based on the proposed method, an initial granular assembly with any desired relative density can be obtained, which can be used for mesoscopic simulation of grained materials.