This paper presents an achievable rate optimization approach for large stacked intelligent metasurfaces (SIMs) using statistical channel state information (CSI). The proposed method focuses on maximizing the downlink achievable rate in a multiuser communication system, where the SIM enables wave-based processing to reduce energy consumption and hardware costs. Unlike previous works that use instantaneous CSI, this study considers statistical CSI to overcome the challenges of large overhead. The SIM is composed of multiple layers of metasurfaces, each with a large number of meta-atoms, and the optimization is performed using an alternating optimization (AO) algorithm that adjusts the phases of the SIM and the allocated transmit power. The simulations demonstrate the performance of the SIM-assisted design and the comparison between different CSI considerations. The key contributions include the derivation of a tractable expression for the downlink achievable rate based on large-scale statistics and the proposal of an AO algorithm that optimizes the phase shifts and transmit power. The results show that the proposed method achieves lower overhead and better performance compared to instantaneous CSI. The algorithm converges quickly and has low computational complexity, making it suitable for practical implementation. The numerical results confirm the effectiveness of the proposed approach in improving the sum SE of large SIM-assisted multiuser communications.This paper presents an achievable rate optimization approach for large stacked intelligent metasurfaces (SIMs) using statistical channel state information (CSI). The proposed method focuses on maximizing the downlink achievable rate in a multiuser communication system, where the SIM enables wave-based processing to reduce energy consumption and hardware costs. Unlike previous works that use instantaneous CSI, this study considers statistical CSI to overcome the challenges of large overhead. The SIM is composed of multiple layers of metasurfaces, each with a large number of meta-atoms, and the optimization is performed using an alternating optimization (AO) algorithm that adjusts the phases of the SIM and the allocated transmit power. The simulations demonstrate the performance of the SIM-assisted design and the comparison between different CSI considerations. The key contributions include the derivation of a tractable expression for the downlink achievable rate based on large-scale statistics and the proposal of an AO algorithm that optimizes the phase shifts and transmit power. The results show that the proposed method achieves lower overhead and better performance compared to instantaneous CSI. The algorithm converges quickly and has low computational complexity, making it suitable for practical implementation. The numerical results confirm the effectiveness of the proposed approach in improving the sum SE of large SIM-assisted multiuser communications.