Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.35. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature. packing, binary mixture, sphere, spherocylinder, packing density, aspect ratio PACS: 45.10.Na, 45.70.Cc, 81.05.RmThe sphere and spherocylinder are both important 3D objects and were widely involved in packing investigations and engineering practices. The sphere is the earliest and the most comprehensively studied shape in packing investigations. Weitz [1] listed some important packing densities for identical spheres, where the density is about 0.64 for random close packing and 0.56 for random loose packing. A spherocylinder is a capsule like object which consists of a cylinder and two hemispheres on both sides. The shape of a spherocylinder is usually described by an aspect ratio w = H/D, where H is the height of the cylinder part and D is the diameter. When w = 0, a spherocylinder degenerates to a sphere. The spherocylinder is one of the well-studied non-spherical shapes, since it has a smooth surface and is easy to be described by mathematical functions or a sphere assembly model. In general, the simulation results on the random packing of spherocylinders in literature [2][3][4][5][6][7] are quite consistent, the maximum packing density is around 0.69 ~ 0.7 when w ≈ 0.4.The densest packing has always been an important objective of packing investigations and it is generally measured by the packing density Φ. A mixture of particles with different sizes can give a much higher packing density than mono-sized particles and is widely applied in engineering. The mixture packing density, that is the packing density of the mixture, is dependent on many factors, e.g. the packing density of each component, particle size distribution, volume fraction and particle shape. Among these factors, the influence of particle size distribution ha...