The main objective of the present work is to present and discuss the effects of the residual stresses generated in the matrix. Both, elastic and elastic-plastic models using explicit finite element code Abaqus were developed to investigate the thermal residual stresses generated around a diamond particle embedded in a metal matrix (a binder) during the sintering process for obtaining a diamond tool. The first part of the work consists in examining the thermal residual stress field generated by using three sintering temperatures from which the bodies are cooled from (T1=800°C, T2=700°C and T3=600°C) and two diamond shapes modelled with 2D axisymmetric elements, one from a circle the other from an octagon, respectively. In this case only one type of binder showing typical elastic behaviour is considered. The second part of this work consists in comparing the finite element solutions using binders with different tensile behaviour (elastic vs. elastic-plastic behaviour). This last study has used a particle shape generated from the octagon, since this shape allows, in a great number of real situations, the simulation of a particle with a larger number of facets, in line with what it is observed when looking at a conventional diamond tool.