A growing number of applications require high capacity, high throughput tertiary storage systems. We are investigating how data striping ideas apply to arrays of magnetic tape drives. Data striping increases throughput and reduces response time for large accesses to a storage system. Striped magnetic tape systems are particularly appealing because many inexpensive magnetic tape drives have low bandwidth; striping may offer dramatic performance improvements for these systems. There are several important issues in designing striped tape systems: the choice of tape drives and robots, whether to stripe within or between robots, and the choice of the best scheme for distributing data on cartridges. One of the most troublesome problems in striped tape arrays is the synchronization of transfers across tape drives. Another issue is how improved devices will affect the desirability of striping in the future. We present the results of simulations comparing the performance of striped tape systems to non-striped systems.