Abstract: By using the limit analysis upper bound theorem, the elastic solution of dynamic Brazilian tests is optimized. Considering the effects of the radially angled cracks caused by the high-speed impact at contact points of the disk on the dynamic tensile strength, a new formula for computing the upper bound solution of the limit dynamic tensile strength is obtained. The original elastic solution and new upper bound solution are discussed by analyzing the dynamic tensile results of sandstone. The research shows that the dynamic tensile properties of sandstone do not change significantly with the loading rate. With the increase of the loading rate, the curve of dynamic tensile strength is relatively flat. The upper bound solution offers a more secure and reliable reference value for the use of sandstone rock mass.