To ensure the normal use of concrete slab structures, it is important to understand the impact fracture characteristics of concrete slabs. In this paper, the fracture processes of concrete slabs under different hammerhead shapes, impact velocities and concrete strengths are simulated based on a continuum-discontinuum element method (CDEM), and the fracture mechanisms of concrete slabs are discussed by analyzing the fracture forms, fracture degree, hammerhead stress and support reaction. The research results show that concrete slabs with lower tensile strength and larger cohesion easily generate bifurcation and unidirectional cracks due to impact tensile failure. However, concrete slabs with larger tensile strength and smaller cohesion are prone to generate dispersion cracks due to impact shear failure. As the tensile strength increases and the cohesive strength decreases, the fracture degree of the concrete slab under impact loading increases from 0.00795 to 0.01434; however, the impact reaction of the support slab markedly decreases from 53,998 N to 47,636 N, which indicates the bearing performance of fracture concrete slab increases. With an increasing of impact velocity (3 ∼ 5 m/s), the dynamic responses of concrete slab are more obvious, the final fracture degree of the concrete slab linearly increases from 0.00658 to 0.01587, the impact stress of the hammerhead obviously increases from 1.04e8 to 1.86e8 Pa, and the impact reaction linearly increases from 40,801 N to 57,432 N. For different impact velocities and concrete strengths, the hammerhead shapes also have a significant influence on concrete fracture. In conclusion, compared with the impact modes of square and circular hammers, rectangular hammer impact easily directionally fractures the concrete slab structures with different strengths.