Based on the characteristics of the bridge construction accident， the bridge construction safety accident rheological rule curve was drawn by studying on the theory of rheology and mutation bridge construction safety accident law. The bridge construction safety accident rheology and mutation mathematical model was set up， and the cause of the accident and the relationship between rheological mutation curve was analyzed using the mathematical software MATLAB based on the mathematical model. Initial safety and attenuation rate of accident time effect was obtained by means of verify and analysis on the mathematical model. The rheology and mutation mathematical model is proved to be reasonable， through studying on the deformation monitoring data of support structure during construction.