Graphics Processing Units in today’s desktops can well be thought of as a high performance parallel processor. Each single processor within the GPU is able to execute different tasks independently but concurrently. Such computational capabilities of the GPU are being exploited in the domain of Data mining. Two types of Hierarchical clustering algorithms are realized on GPU using CUDA. Speed gains from 15 times up to about 90 times have been realized. The challenges involved in invoking Graphical hardware for such Data mining algorithms and effects of CUDA blocks are discussed. It is interesting to note that block size of 8 is optimal for GPU with 128 internal processors.