energy deposition into targets and beam absorbers in high-energy accelerator leads to temperature rise at an enormous rate, giving rise to thermally induced stress waves. Understanding and predicting resulting stresses are crucial for robust design and safe operation of such devices. In this paper, a closed form expressions for the induced stresses in cylindrical rods subjected to rapid partial energy deposition have been directly derived; it is then used to estimate highest stress of long cylindrical absorbers and to test the accuracy of thermal shock simulation with Finite Element Analysis (FEA) codes. Characteristics of such stresses were discussed in detail. It was found that ANSYS may produce accurate details in thermal shock simulation if element size and time step used in simulation model meet the criteria proposed by Zheng etc. in another paper.