In this study, a simulation for two story building associated with a vertical solar chimney was made by using ANSYS 2022/R1. The study conducted under the climatic conditions of Al-kut city/ Iraq on 5/8/2016. The study involved a comparison between the ventilation performance of SC before and after adding Energy Storage. Al-dura, RT-42, and block-shaped paraffin wax were the three types of PCM that were studied in order to find the optimum ES. The numerical results showed that the best Paraffin wax was Al-dura depending on the average Air Change per Hour (ACH), average indoor temperature, and the ventilation period after sunset. Comparing with the 1st model (without ES), After adding Al-dura wax, the ACH increased by 18.3 % and 9.95 % for 1st and 2nd floor, respectively. whereas, the indoor temperature was reduced by 1.17 k and 0.68 k on the 1st and 2nd floor, respectively. As for the ventilation period, it was  lasted for 5 h after sunset.