The dynamic response of concrete components under blast loading is of great military and social importance. Based on the continuum-discontinuum element method and fluid–structure coupling algorithm, the dynamic response of concrete slab is simulated and analyzed. First, a full-time numerical simulation is conducted. Then, the displacement and crack characteristics of concrete slab are analyzed quantitatively. The result indicates that the displacement is distributed in a circular pattern, and the maximum value is located at the center of concrete slab. The crack ratio increases gradually with the growth of time, while the growth rate is not a constant value. The fracture type of concrete slab includes tensile fracture and shear fracture, the interface at the center mainly undergoes shear fracture, and a small number of interface on the outside of cracked region suffers tensile fracture.