Dynamic bifurcation buckling of an elastic straight rod under stress wave were studied. Numerical method, which unifies both the idea of twin-characteristic-parameters method and method of the preferred mode, was established. The method can be used to solve buckling of rod under time-varying load, with a unified buckling discriminate form for dynamic buckling under stress wave caused by both step load and time-varying load. Calculation results predicted by this method are in good agreement with the experimental results.