We measured the Raman spectrum associated with the E2-TO(quasi) and LO(quasi) modes of 6H-SiC particles as a function of hydrostatic pressure using a diamond anvil cell. The results of this calibration experiment were used to analyze the residual stress in 6H-SiC particles within Al2O3/SiC composites with 12%, 20%, and 30% SiC by volume. The Raman spectra show that residual stress in the SiC near the surface of the composites is -2040 +/- 120, -1841 +/- 110, and -1615 +/- 100 MPa for the 12%, 20%, and 30% SiC composites, respectively. The measured decrease in stress with increasing packing fraction is consistent with theoretical predictions based on micromechanics.