Solid State Devices (SSDs) have been widely adopted in containerized cloud platforms as they provide parallel and high speed data accesses for critical data-intensive applications. Unfortunately, the I/O stack of the physical host overlooks the layered and independent nature of containers, thus I/O operations require expensive file redirect (between the storage driver, Overlay2/EXT4, and the virtual file system, VFS) and are scheduled sequentially. Moreover, containers suffer from significant I/O contention as resources at the native file system are shared between them. This paper presents a Container-aware I/O stack (CAST). CAST is made up of Layer-aware VFS (LaVFS) and Container-aware Native File System (CaFS). LaVFS locates files based on layer information and enables simultaneous copy-on-write (cow) and thus avoids the overhead of searching and modifying files. CaFS, on the other hand, provides contention-free access by designing fine-grain resource allocation at the native file system. Experimental results using a NVMe SSD with micro-benchmarks and real-world applications show that CAST achieves 216%-219% (38%-98%, respectively) improvement over the original I/O stack.