This research aims to estimate production functions through which production relations, possibilities for production elements substitution, measurement of its substitution elasticity, and efficiency and distribution coefficients can be analyzed. This would be done through estimation of constant elasticity of substitution production function for agricultural companies in Iraq depending on data from Iraqi Stock Exchange reports of 2005-2016. The researcher had used panel data model and estimated its three models: the Pooled Regression Model (PRM), the Fixed Effect Model (FEM) and the Random Effect Model (REM). A comparison was made for theses three models using F, LM, Husman tests. Tests show that Fixed Effect Model (FEM) is the best estimated one and depended as the explanation of the constant elasticity of substitution production function. The results of this function referred that a 1% increase in capital stock and labor would increase the agriculture production of the agricultural companies with 0.73 and 0.48 % respectively. The capital stock helps in using the production technology. Also, there were no indications that the production technology effects on production value (i.e there is no increasing in efficiency value with the increasing of capital stock; note that the timeline of the study was 12 years in which supposed to show the applied production technology used by the agricultural companies and if it happened, it would be of no important. The elasticity substitution was 10, which is high and indicates that there are other substitutions available to the companies.  The researcher recommends to put the scientific resources management, the changing of production and competence, the information technology, and the market changes into consideration so as to have a great competent.