Using elastic plates in combination with counter-flow heat exchangers is an innovative aspect of thermal energy storage systems (TES). The incorporation of elastic plates greatly enhances heat transfer. However, prior studies have not thoroughly investigated the effects of exerting force on these elastic plates. The flow and heat transfer in a counter-flow plate heat exchanger with elastic parts on the lower and upper plates are numerically investigated in the current study. The study employs fluid-structure interaction (FSI) modeling to account for the elastic behavior of these plates, with external forces applied downward on the upper plate and upward on the lower plate. In this study, five different heat exchangers are simulated. There are two elastic plates in all these heat exchangers. These elastic plates are located in different positions. The results show that the efficiency of all these heat exchangers is greater than the heat exchanger without the elastic plate. The efficiency increased between 17% and 140%. The maximum increase is seen in the heat exchanger B. In this heat exchanger two elastic plates opposite each other and in the middle of the heat exchanger. The results also showed that the rate of heat transfer rate in the converter was up to 5 % more than other converters. Results show heat transfer rate for case B is up tp 30% higher than the other configurations. Also, the results demonstrate that tripling the Reynolds number leads to a 47% increase in the efficiency for case B. External force exerted on elastic plate to increase the heat transfer rate, but according to the results, the heat transfer rate has varied only 4% with the doubling of the external force. The implications of these findings have significance for designing heat exchangers with higher efficiency, offering potential improvements for condensers, evaporators, and boilers.