A tube bundle heat exchanger is a typical heat exchange equipment that exchanges heat between two fluids with different temperatures. Through this equipment, one fluid can be cooled down and another fluid can be heated up to meet their respective needs. The equipment is widely used in chemical, petroleum, pharmaceutical, energy, and other industrial sectors, and is one of the indispensable and important equipments in chemical production. To improve the heat transfer performance and service life of the heat exchanger, a numerical analysis of the vibration response of the elastic tube bundle in the heat exchanger based on fluid–structure coupling analysis is proposed. Using the weak coupling method of fluid–structure coupling, the vibration response of multiple rows of elastic tube bundles induced by shell side fluid in a heat exchanger with different tube row spacing and different tube row numbers is studied numerically, and the effects of shell side fluid and tube side fluid on the vibration response of elastic tube bundles are compared and analyzed. The results show that the maximum relative error of monitoring point amplitude is 43.36% when H = 40 mm and 10.17% when H = 70 mm. For connection IV, the maximum relative error of monitoring point amplitude is 31.71% when H = 40 mm and 24.08% when H = 70 mm. This is because when H is small, the interaction between rows of tube bundles is strong, so the amplitude changes violently with the number of the tube bundle. The step-by-step calculation strategy of rough calculation and actuarial calculation proposed in this article can greatly reduce the calculation time and improve the calculation efficiency.