The X-ray elastic constants of composite ceramics of ziruconia mixed with 40wt% alumina wee determined by X-ray stress measurements and compared with theoretical perdiction. The results obtained are summarize as follows: (1) The X-ray elastic constants were determined for the diffraction from Al_2O_3 (1 4 6) plane by Cu-Kα radiation, and for those from Al_2O_3 (1.0.10) and ZrO_2 (1 3 3) planes by Cr-Kα radiation. The X-ray values of E_x'/(1+ν_x') and E_x'(E_x'=Young's modulus, ν_x'=Poisson's ratio) of the composite decreased in the alumina phase and increased in the zirconia phase when compared with those of single-phase ceramics. (2) The values of E_x'/(1+ν_x') for Al_2O_3(1 4 6), Al_2O_3(1.0.10) and ZrO_2(1 3 3) planes of the composite calculated from those of single-phase ceramics on the bases of Hauk's model agreed fairly well with the experimental values. The value of E_x' /(1+ν_x') for the alumina phase in the composite calculated from the elastic constants of single crystals on the basis of Eshelby's model was slightly larger than the experimental value. The contribution of pores in the composite should be included in modeling.