Abstract: Considering the length of the subcritical growth of the main crack and the cohesive strength of the fictitious crack of concrete, and using the analytical relationship between the J integral and the stress intensity factor, a numerical algorithm based on the element free Galerkin method with wavelet basis to solve the equivalent fracture toughness of concrete is proposed, and the influence of different resolutions of wavelet basis on the calculated values of the equivalent fracture toughness of concrete is investigated. The calculated results for the equivalent fracture toughness of concrete of 8 specimens with cracks show that in the case of the identical resolution of wavelet basis, the mean square deviations and the coefficients of variation of the calculated values of the 4 specimens with different volumes are smaller than 0.0244 and 0.0231, respectively, and the mean square deviations and the coefficients of variation of the calculated values of the 4 specimens with different heights are smaller than 0.0384 and 0.0362, so the consistency of the calculated results is satisfactory. By comparing with the analytical solutions, the maximum relative error of the calculated values of 8 specimens is about 5%, so the accuracy of the calculated results is high. And the influence of different resolutions of wavelet basis on the calculated results is small. A conclusion is given that the element free Galerkin method with wavelet basis is a reliable numerical algorithm with high precision to solve the equivalent fracture toughness of concrete, and may be taken as a powerful calculation tool in the fracture mechanics of concrete.