To explore the influence of randomness of materials and loads on the crack driving force of TP304 stainless steel, a probability prediction for crack driving force through the elastic-plastic finite element method (EPFEM) coupled with the Kriging surrogate model was proposed. To improve the efficiency of finite element analysis, MATLAB was used to further develop the pre-processing and post-processing procedures of ABAQUS software to realize the automatic change of random specimens, batch calculation, and automatic analysis of probability prediction results. The statistical distribution law of the crack driving force of TP304 stainless steel material under the action of random factors was obtained, as well as other probability characteristics, including failure probability, failure probability density function, cumulative probability density function, etc. The sensitivity of each random factor was analyzed. Finally, the effectiveness and efficiency of the proposed method were analyzed, compared with those of the Monte Carlo method. Results show that the randomness of load and material parameters can significantly influence the driving force of crack tips of TP304 stainless steel, thereby affecting the failure probability of TP304 stainless steel. The load and strain hardening exponent present the most obvious effect on the dispersion of crack driving force of austenitic TP304 stainless steel.