Grain boundaries(GB) play an important role in the deformation behaviour of polycrystalline materials. They are often considered as regions of stress concentrations and potential sites for crack nucleation. In continuum scale modelling deformation of polycrystalline materials, GBs are not explicitly considered. They are typically represented by the orientations of the grains abutting them. There is often no explicit accounting for the intricate nature of the grain boundaries themselves. This is because it is challenging to assign quantities to GBs that are often used in continuum scale simulations such as stress tensor. There is no definite answer to the question: What is the stress state of a grain boundary? In this work, we set out a methodology to answer this question and apply it for a few well defined GBs. First, the GBs are assumed to be made up of dislocations which may be described by a network of these dislocations. Using the Frank-Bilby relationship the characteristics of the dislocation networks i.e. line vectors, Burgers vectors and the spacing between them, are identified. The equilibrated stress fields corresponding to these networks are then obtained by employing the field dislocation mechanics(FDM) approach. Fast Fourier transformation(FFT) based method is used to solve the equations arising in FDM. Both low angle grain boundaries and few high angles grain boundaries are studies using the above method. The decay of the local stress fields and how they are influenced by the disorientation angle are reported. Further, the role of elastic anisotropy on the observed stress field are discussed.