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The characteristics of dynamic strength and deformation on rock with different axial pre-compressions under cyclic impacts were conducted with modified split Hopkinson pressure bar (SHPB). Firstly, the different axial pre-compression stresses were loaded on sandstone specimens before the cyclic impact loadings were carried on. And then, the typical dynamic stress-strain curve of specimen under cyclic impacts was investigated. Finally, the characteristics of dynamic strength and deformation of rock with different axial pre-compressions were studied during cyclic impacts. The results show that, with the increase of number of cycle impacts, the deformation modulus of loading stage and the first unloading stage, transmitted wave and peak stress, the ratio of recovered strain and peak strain, the ratio of recovered stress and critical unloading stress reduce gradually. While, the average strain rate, peak strain, the deformation modulus of the first unloading stage, and specific energy absorbency increase gradually. When the axial compression of rock is 22%, 51% and 65% of its uniaxial compressive strength, the relation between the ability of resistance against cyclic impacts and the cycle-index is from slow development to sharp decline. When the axial compression of rock is 0 or 65% or 87% of its uniaxial compressive strength, the ability of resistance against cyclic impacts drops constantly during the whole cycle. The rock's ability of resistance against the cyclic impacts is highest when the axial compression of rock is 22% of its uniaxial compressive strength. [ABSTRACT FROM AUTHOR]