How to deal with used rubber has become a difficult problem worldwide. Adding powdered used tires in certain grain sizes to cement concrete can modify cement concrete, which is also a nuisance-free treatment and rational utilization thereof. In the early stage of research work, the author found that the rubber concrete mixed with fine used rubber powder whose grain diameters are 80, 100, 120 meshes showed a good anti-freeze durability. Based on these, the basic mechanical properties of rubber concrete within that grain size range are studied in this paper. The relations between axial compressive strength and cubic compressive strength, splitting tensile strength and cubic compressive strength are established to provide a design basis for engineering applications.