In this paper a cohesive formulation is proposed for modelling intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model uses a multi-region boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic orthotropic behaviour and specific material orientation. Transgranular surfaces are inserted as the simulation evolves and only in those grains that experience stress levels high enough for the nucleation of a new potential crack. Damage evolution along (inter- or trans-granular) interfaces is then modelled using cohesive traction separation laws and, upon failure, frictional contact analysis is introduced to model separation, stick or slip. This is the first time inter- and trans-granular fracture are being modelled together by BEM, and DBEM is being extended to include cohesive approach for anisotropic materials. Finally numerical simulations are presented to demonstrate the validity of the proposed formulation in comparison with experimental observations and literature results.