The stress field existing within a polycrystalline material can be described at different scales of interest. Here, the stresses for two different scales are considered: the macro stress which is defined as the average stress over the sample volume containing a large number of polycrystalline grains, i.e. over many millimeters or even centimeters; and the second order stress which is defined as the deviation of the stress for a particular grain from the macroscopic value. The second order stresses vary on the scale of the grain size, or the inter-particle spacing in composite material. In this work the second order stress was predicted using the self-consistent model of elasto-plastic deformation for Al/SiCp composite. The results were verified using neutron diffraction method of stress measurement.