We have introduced a Multi-Dimensional Clustering (MDC) physical layout scheme in DB2 version 8.0 for relational tables. Multi-Dimensional Clustering is based on the definition of one or more orthogonal clustering attributes (or expressions) of a table. The table is organized physically by associating records with similar values for the dimension attributes in a cluster. Each clustering key is allocated one or more blocks of physical storage with the aim of storing the multiple records belonging to the cluster in almost contiguous fashion. Block oriented indexes are created to access these blocks. In this paper, we describe novel techniques for query processing operations that provide significant performance improvements for MDC tables. Current database systems employ a repertoire of access methods including table scans, index scans, index ANDing, and index ORing. We have extended these access methods for efficiently processing the block based MDC tables. One important concept at the core of processing MDC tables is the block oriented access technique. In addition, since MDC tables can include regular record oriented indexes, we employ novel techniques to combine block and record indexes. Block oriented processing is extended to nested loop joins and star joins as well. We show results from experiments using a star-schema database to validate our claims of performance with minimal overhead.