This paper demonstrates a significant long-run relationship between area and productions of Food grain crops grown in India during the period 1950-2018. Stability of the estimated model parameters are studied . To assess the consistency of the model parameters the cumulative sum of recursive residuals test and the cumulative sum of recursive residuals squares tests are used.Additionally, cointegration equations such as the Fully Modified Ordinary Least Square Dynamic Ordinary Least Squares, and Canonical Cointegration Regression are applied to check the long-run elasticities in the concerned relationship.