Concrete　structures　in　extremely　cryogenic　environments　may　be　subject　to　dynamic　loadings　as　a　result　of　occasional　accidents　or　terrorist　attacks　during　the　service　life.　Considering　the　cryogenic　temperature　effect　and　strain　rate　effect　of　each　phase　for　concrete,　a　meso-scale　numerical　model　of　the　concrete　subjected　to　cryogenic　temperature　and　dynamic　loadings　was　presented　in　this　study,　which　serves　as　a　preliminary　foundation　for　calculating　and　evaluating　the　performances　of　concrete　structures　at　cryogenic　temperature.　Taking　concrete　cube　as　an　example,　the　dynamic　compressive　behavior　and　strain　rate　effect　of　concrete　specimens　at　cryogenic　temperature　from　20　degrees　C　to　-160　degrees　C　were　modelled　and　investigated.　The　numerical　results　indicate　that　the　failure　appearances　and　compressive　strength　are　highly　related　to　the　cryogenic　temperature　and　dynamic　loadings.　The　compressive　strength　at　cryogenic　temperature　is　greater　than　that　at　ambient　temperature,　and　the　sensitivity　of　dynamic　compressive　strength　to　strain　rate　is　enhanced　at　cryogenic　temperature.　Moreover,　the　absorbed　energy　and　dynamic　elastic　modulus　tend　to　increase　with　the　decrease　of　temperature　and　increase　of　strain　rate.　According　to　the　numerical　results,　an　empirical　formula　on　dynamic　increase　factor　of　compressive　strength　at　cryogenic　temperatures　(CDIF　(T)　)　was　established.