To promote the application of rubber-cement composites as the main bearing structure and key components in practical engineering under frequent dynamic disturbances, in this work, the split Hopkinson pressure bar (SHPB) cyclic impact tests of rubber-cement composite specimens with four different confine modes were carried out in which the impact load increased sequentially. The relationship between average strain rate, ultimate strain and impact times and the relationship between peak stress, damage energy, ultimate strain and incident energy were analyzed. The results showed that the appropriate confine reinforcement treatment can make rubber-cement composite give full play to its deformation ability when it was completely damaged. Carbon fiber-reinforced polymer (CFRP) sheet and steel cylinder can work together with the rubber-cement composite matrix to resist impact load, which effectively improves the structural strength, damage fracture energy, and cyclic impact resistance of the rubber-cement composite. Finally, based on the effect difference of confine modes, the simplified plane force models of rubber-cement composite specimens with four different confine modes were established, which clearly revealed the completely different impact resistance mechanism of the rubber-cement composites with different constraints under cyclic impact loading.