The main objective of this study is to propose the generalized least squares estimation of stochastic linear regression model with non- spherical errors. In addition to this work the problems of stochastic linear regression model have been presented here. Generalized least squares (GLS) estimators have a wide number of applications in dealing with the inferential problems of stochastic linear regression models especially in the case of the problems of Heteroscedastic errors and Auto correlated errors. NimetOzbayetal [1], in 2018, in their paper proposed the weighted mixed regression estimation of the coefficient vector in a linear regression model with stochastic linear restrictions binding the regression coefficients. In 1980 P.A.V.BSwamy etc.al [2] proposed a linear regression model where the coefficient vector is a weakly stationary multivariate stochastic process and that model provider a convenient representation of a general class of non-stationary processes. They proposed prediction and estimation methods which are linear and easy to compute. Danjiang He et.al [3] in 2014, in their paper proposed a new estimator to combat the multicollinearity in the linear model when there are stochastic linear restrictions on the regression coefficients and the new estimator arcs constructed by combine's the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator which is called the stochastic restricted principal components (SRPC) regression estimator. In 2014, Shuling Wang et al [9], in their paper proposed some diagnostic methods in stochastic restricted linear regression models. Gil Ganjalez et al [10] in 2007, in their paper derived the least squares estimators for the simple estimators for the simple linear regression model and examined them from a theoretical perspective. © 2019 Author(s).