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Recent nuclear proliferation concerns and disarmament agreements have encouraged the U.S. to decrease the excess amount of weapons-grade and reactor-grade plutonium. Continued use of nuclear power without a permanent solution for waste disposition has also led to the need for a reliable method by which the waste products, specifically plutonium, can be utilized or destroyed. One possible solution to plutonium destruction is achieved by manufacturing it into small microspheres and embedding it within an inert metal matrix, then placing it inside a conventional nuclear reactor. This process would burn some of the plutonium while producing electricity. PuO2Zr dispersion fuel has been proposed for such a purpose. Prior to its use, however, this non-fertile metal matrix dispersion fuel must be shown to be mechanically stable in the reactor environment. The internal mechanical interactions of dispersion fuel were modeled using finite element analysis. The results were used to assess the stability of PuO2Zr dispersion fuel inside a reactor. Several parameters, including fuel particle size, volumetric loading, temperature, and burnup, were varied to determine the maximum amount of plutonium that can be burned while maintaining fuel integrity. Earlier experiments using UO2 stainless steel dispersion fuels were used to validate the model and establish a failure criterion. The validated model was then used to determine the parameter space over which PuO2Zr dispersion fuel can be successfully used. These results show that PuO2Zr dispersion fuel is robust and may offer a reliable method for plutonium disposal in current reactors.