The Hierarchical model has been discussed and implemented from Bayesian viewpoint. The mixed effects models lack statistical and philosophical grounds and Bayesian approach is the only remedy for such models. Bayesian statistics is an excellent alternative to be more reasonable for moderate and especially for small sample sizes when non Bayesian procedures do not work (e.g., Berger 1985, page 125). In this paper we have made Bayesian analysis of Hierarchical Models and illustrated its application in agriculture. Advancement in the computational power of high speed computers has aided the application part. Suitable illustrations have been proposed on real data set generated on potato crop in year 2005-2006 at five different locations with twelve genotypes in SKUAST-(K).