Rivet lap joint is a typical structure susceptible to multi-site damage, which is prone to initiate rivet holes-edge crack. It significantly threatens the safety of aircraft structures. Due to the randomness of the crack number, position, size, there exists a complex contact relationship between rivets and plates. In order to efficiently and accurately calculate the stress intensity factor of multi rivet lap joint structures for crack propagation life analysis, a weight function analysis method for rivet lap joint structure is proposed to address the complex crack issues in lap joint structures. Firstly, the crack configurations of rivet lap joint structures are reasonably simplified and classified, the corresponding weight functions are used to calculate the stress intensity factors of different crack configurations. Then, finite element analysis is conducted to compute the stress intensity factor to validate the accuracy of the weight function method. Finally, combined with the Paris crack growth formula, fatigue crack growth of the rivet lap joint structures are predicted, and the effectiveness of the present method is verified by experiments. The results show that the relative difference between the stress intensity factor calculated by the weight function method and the finite element method is less than 5%. The predicted crack growth life is in good agreement with the test results, and the computational efficiency is three orders of magnitude faster than that of the finite element method. This paper provides an effective method for the stress intensity factor and fatigue crack growth analyses of rivet lap joint structures.