Abstract We present an out-of-core hydrodynamic code for high resolution cosmological simulations that require terabytes of memory. Out-of-core computation refers to the technique of using disk space as virtual memory and transferring data in and out of main memory at high I/O bandwidth. The code is based on a two-level mesh scheme where short-range physics is solved on a high-resolution, localized mesh while long-range physics is captured on a lower resolution, global mesh. The two-level mesh gravity solver allows FFTs to operate on data stored entirely in memory, which is much faster than the alternative of computing the transforms out-of-core through non-sequential disk accesses. We also describe an out-of-core initial conditions generator that is used to prepare large data sets for cosmological simulations. The out-of-core code is accurate, cost-effective, and memory-efficient and the current version is implemented to run in parallel on shared-memory machines. I/O overhead is significantly reduced down to less than 10% by performing disk operations concurrently with numerical calculations. The current computational setup, which includes a 32 processor Alpha server and a 3 TB striped SCSI disk array, allows us to run cosmological simulations with up to 4000 3 grid cells and 2000 3 dark matter particles.