The yard layout significantly influences the performance of automated container terminals (ACTs), especially those employing a perpendicular stack configuration, where the yard blocks are perpendicular to the quay line. Thus, this study is dedicated to optimizing the yard layout tailored for ACTs with such configurations. First, we develop cycle time formulas for the automated stacking crane (ASC) by considering the dependency between its successive handling operations, highlighting the impact of the previous operation on the subsequent one. Further, to address the interferences between the two ASCs within a yard block, a novel hybrid simulation-analytical approach is proposed. Then, utilizing the derived ASC cycle time formulas, an analytic model is constructed based on the G1/G/1 queuing theory to optimize the yard layout design parameters (including the number of yard blocks, bays per block, and rows and tiers per bay) from the perspective of both cost-effectiveness and operational efficiency. In the numerical experiments, optimal yard layouts for two ACTs of different sizes are generated by utilizing the analytic model, and design insights are derived through the sensitivity analysis. The experiments underscore the importance of considering the dependency between successive handling operations and ASC interferences in the design of yard layouts for ACTs.