Rendering volume represnted as a 3D grid of voxels requires on overwhelming amount of processing power. In this paper we investigate efficient technies for rendering semi-transparent volumes on vector and parallel processors. Parellelism inhernt in a regular grid is obtained by decomposing the volume into geometric primitives called beams, slices and slabs of voxels. By using the adjecency properties of voxels in beams and slices, efficient incremental transformation schemes are developed. The slab decoposition of the volume allows the implementation of an efficient parallel feed-forward renderer which includes the spaltting technique for image reconstruction and a implementation of theis feed-forward volume renderer on a hierarchical shared memory machine with individual pipelined processors