Multiplicity of the effective factors in drilling reflects the complexity of the interaction between rock mass and drilling bit, which is followed by the dependence of parameters and non-linear relationships between them. Rock mass or, in other words, the formation intended for drilling, as the drilling environment, plays a very essential role in the drilling speed, depreciation of drilling bit, machines, and overall drilling costs. Therefore, understanding the drilling environment and the characteristics of the in-situ rock mass contributes a lot to the selection of the machines. In this work, a 1D geo-mechanical model of different studied wells is built by collecting the geological data, well logs, drilling data, core data, and pressure measurements of the formation fluid pressure in various wells. Having the drilling parameters of each part of the formation, its specific energy is calculated. The specific energy index can be used for predicting the amount of energy consumed for drilling. In order to find the relationship between the drilling specific energy (DSE) and its effective parameters, the multivariate regression model is used. Modeling DSE is done using the multivariate regression, which contains the parameters rock characteristics, well logs, and a combination of these two features. 70% and 30% of the data are, respectively, selected as the training and test for validation. After analyzing the model, the correlation coefficients obtained for the training and test data were, respectively, found to be 0.79 and 0.83. The parameters uniaxial compressive strength (UCS), internal friction angle, and fluid flow are among the most important factors found to affect DSE.