Numerical simulations were conducted to investigate the potential energy savings as a result of using Phase Change Materials (PCMs) in the wall and roofing systems of single-zone buildings when these buildings were subjected to the weather conditions of Kuwait City. In accordance with the requirements of the Kuwaiti Building Energy Code, six Window-to-Wall Ratios (WWRs) of the main solar-oriented window facade were considered, where the ranges of WWR, U-factor, and Solar Heat Gain Coefficient (SHGC) were 10–70%, 1.71–3.42 W/(m²K), and 0.23–0.36, respectively. The results show that a melting temperature of 24 °C for PCM-drywalls has resulted in the lowest energy loads. Also, the results show that the contributions to the yearly cooling loads for buildings with PCM-drywalls in the different cardinal directions are, respectively, 17.6–20.5% and 4.0–7.9% lower than that for buildings without drywall and buildings with drywall but without PCM. Where the windows are located in the four cardinal directions for single-zone buildings, the results showed that the window case having WWR = 10%, U-factor = 3.42 W/(m²K), and SHGC = 0.36 results in the lowest yearly total loads. However, the window case having WWR = 40%, U-factor = 3.38 W/(m²K), and SHGC = 0.254 results in the highest yearly total loads. Finally, the results show that the months of the highest energy loads occurred in July and August. However, the months of the lowest energy loads depend on the cardinal direction of the window and wall systems.