System developments and research on parallel query processing have concentrated either on "Shared Everything" or "Shared Nothing" architectures so far. While there are several commercial DBMS based on the "Shared Disk" alternative, this architecture has received very little attention with respect to parallel query processing. This paper is intended as a first step to close this gap. A detailed comparison between Shared Disk and Shared Nothing reveals many potential benefits for Shared Disk with respect to parallel query processing. In particular, Shared Disk supports more flexible control over the communication overhead for intratransaction parallelism, and a higher potential for dynamic load balancing and efficient processing of mixed OLTP/ query workloads. We also outline necessary extensions for transaction management (concurrency/coherency control, logging/recovery) to support intratransaction parallelism in the Shared Disk environment.