Based on the experiment results, the damage and fracture behavior of concrete at the ages of 1d, 2d, 7d and 28d, in three-point bending and uniaxial tensile tests, were simulated with a finite element program, ABAQUS. The critical stress intensity factor $K_{IC}^s$ and the critical crack tip opening displacement ($CTOD_C$) of concrete were calculated with effective-elastic crack approach for the three-point bending test of grade C30 concrete. Based on the crack band model, a bilinear strain-softening curve was derived to simulate the LOAD-CMOD curves and LOAD-Displacement curves. In numerical analysis of the uniaxial tension test of concrete of grade C40, the damage and fracture mechanics were combined. The smeared cracking model coupling with damaged variable was adopted to evaluate the onset and development of microcracking of uniaxial tensile specimen. The uniaxial tension test was simulated by invoking the damage plastic model which took both damage and plasticity as inner variables with user subroutines. All the numerical simulated results show good agreement with the experimental results.