The purpose of this discourse is to describe the estimation methods of COBB-DOUGLAS production functional model thrash cost function and with multiplicative and additive errors. Nonlinear regression models have been a subject of an intensive investigation in select years. It is no exaggeration to say that in Econometric analysis, the COBB-DOUGLAS and constant Elasticity of substitution (CES) functions are the most frequently used non-linear type of special functions. Mohammad Zakir Hussain et al, in 2010, in their research article discussed the use of Cobb-Douglas production model on some selected manufacturing industries. Md.Moyazzem Hossain et al in 2015, in their research paper estimated the parameters of Cobb- Douglas production function with additive errors and multiplicative errors for some selected manufacturing industries and suggested the most suitable Cobb-Douglas production function to forecast the production process for some selected manufacturing industries for developing countries. Besides they investigated the efficiency of both capital and labor elasticity of the two mentioned form of Cobb-Douglas production function. In 1975, DE-Min Vu in his research paper derived the exact distribution of the indirect least squares estimators of the coefficients of the Cobb-Douglas production function within the content of a stochastic production model of Marshak-Andrews type. In 2017, RVSSN Rao et al, in their research paper, presented various estimation methods for estimating parameters of Cobb-Douglas production functional model. © 2019 Author(s).