The sweep paradigm for volume rendering has previously been successfully applied with irregular grids. This thesis describes a parallel volume rendering algorithm called PARZSweep for regular grids that utilizes the sweep paradigm. The sweep paradigm is a concept where a plane sweeps the data volume parallel to the viewing direction. As the sweeping proceeds in the increasing order of z, the faces incident on the vertices are projected onto the viewing volume to constitute to the image. The sweeping ensures that all faces are projected in the correct order and the image thus obtained is very accurate in its details. PARZSweep is an extension of a serial algorithm for regular grids called RZSweep. The hypothesis of this research is that a parallel version of RZSweep can be designed and implemented which will utilize multiple processors to reduce rendering times. PARZSweep follows an approach called image-based task scheduling or tiling. This approach divides the image space into tiles and allocates each tile to a processor for individual rendering. The sub images are composite to form a complete final image. PARZSweep uses a shared memory architecture in order to take advantage of inherent cache coherency for faster communication between processor. Experiments were conducted comparing RZSweep and PARZSweep with respect to prerendering times, rendering times and image quality. RZSweep and PARZSweep have approximately the same prerendering costs, produce exactly the same images and PARZSweep substantially reduced rendering times. PARZSweep was evaluated for scalability with respect to the number of tiles and number of processors. Scalability results were disappointing due to uneven data distribution.