The effective thermal conductivity of matrix-inclusion-microcrack three-phase heterogeneousmaterials is investigated with a self-consistent micromechanical method(SCM)and a random microstructurefinite element method(RMFEM),In the SCM,microcracks are assumed to be randomly distributed and pen-ny-shaped and inclusions to be spherical,the crack effect is accounted for by introducing a crack density pa-rameter,the effective thermal conductivity is derived which relates the macroscopic behavior to the crackdensity parameter.In the RMFEM,the highly irregular microstructure of the heterogeneous media is accu-rately described,the interaction among the matrix-inclusion-microcracks is exactly treated,the inclusionshape effect and crack size effect are considered.A Ni/ZrO_2 particulate composite material containing ran-domly distributed,penny-shaped cracks is examined as an example.The main results obtained are:(1)theeffective thermal conductivity is sensitive to the crack density and exhibits essentially a linear relationshipwith the density parameter;(2)the inclusion shape has a significant effect on the effective thermal conductiv-ity and a polygon-shaped inclusion is more effective in increasing or decreasing the effective thermal conduc-tivity than a sphere-shaped one;and(3)the SCM and RMFEM are compared and the two methods give thesame effective property in the case in which the matrix thermal conductivity λ,is greater than the inclusionone λ_2.In the inverse case of λ_1<λ_2,the two methods agree as the inclusion volume fraction and crackdensity are low and differ as they are high.A reasonable explanation for the agreement and deviation betweenthe two methods in the case of λ_1<λ_2 is made. The effective thermal conductivity of matrix-inclusion-microcrack three-phase heterogeneous materials is investigated with a self-consistent micromechanical method (SCM) and a random microstructure finite element method (RMFEM), In the SCM, microcracks are assumed to be randomly distributed and pen- ny-shaped and inclusions to be spherical, the crack effect is accounted for by introducing a crack density pa-rameter, the effective thermal conductivity is derived the macroscopic behavior to the crack density parameter. in the RMFEM, the highly irregular microstructure of the heterogeneous media is accu-rately described, the interaction among the matrix-inclusion-microcracks is exactly treated, the inclusionshape effect and crack size effect are considered. A Ni / ZrO 2 particulate composite material containing ran-domly distributed, penny- shaped cracks is examined as an example. The main results obtained are: (1) theeffective thermal conductivity is sensitive to the crack density and exhibits es seince a linear relationship with the density parameter; (2) the inclusion shape has a significant effect on the effective thermal conductiv- ity and a polygon-shaped inclusion is more effective in increasing or decreasing the effective thermal conduc- tivity than a sphere-shaped one ; and (3) the SCM and RMFEM are compared and the two methods give thesame effective property in the case in which the matrix thermal conductivity λ, is greater than the inclusionone λ_2.In the inverse case of λ_1 <λ_2, the two methods agree as the inclusion volume fraction and crackdensity are low and differ as they are high. A reasonable explanation for the agreement and deviation betweenthe two methods in the case of λ_1 <λ_2 is made.