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More and more large amounts of data shared with researchers and workstations worldwide are generated by scientific experiments and engineering applications. High performance grids aim at facilitating the distribution of such data to geographically remote places. For high performance data grids where users require remote access to large files, dynamic replication is an efficient method to improve performance. In this paper, Fast Cascading, a new dynamic replication algorithm, is proposed for the multi-tier Data Grid. The simulation results obtained by Simulator OptorSim which has been modified show that this algorithm can reduce the average response time of data access greatly for random access pattern compared with other algorithms,such as Fast Spread, LRU and Economy-Zipf dynamic replication strategy, and the gain increases with the number of jobs submitted.