A numerical analysis on condensation and coagulation of the metallic species with fly ash particles pre-existing in an incinerator was performed. Waste was simplified as a mixture of methane, chlorine, and small amounts of Pb and Sn. Vapor-phase amounts of Pb- and Sn -compounds were first calculated assuming a thermodynamic equilibrium state. Then theories on vapor-to-particle conversion, vapor condensation onto the fly ash particles, and particle-particle interaction were examined and incorporated into equations of aerosol dynamics and vapor continuity. It was assumed that the particles followed a log-normal size distribution and thus a moment model was developed in order to predict the particle concentration and the particle size distribution simultaneously. Distributions of metallic vapor concentration (or vapor pressure) were also obtained. Temperature drop rate of combustion gas, fly ash concentration and its size were selected as parameters influencing the discharged amount of metallic species. In general, the coagulation between the newly formed metal particles and the fly ash particles was much greater than that between the metal particles themselves or between the fly ash particles themselves. It was also found that the amount of metallic species discharged into the atmosphere was increased due to coagulation. While most of PbO vapors produced from the combustion were eliminated due to combined effect of condensation and coagulation, the highly volatile species, PbCl$_{2}$ and SnCl$_{4}$ vapors tended to discharge into the atmosphere without experiencing either the condensation or the coagulation. For Sn vapors the tendency was between that of PbO vapors and that of PbCl$_{2}$ or SnCl$_{4}$. To restrain the discharged amount of hazardous metallic species, the coagulation should be restrained, the number concentration and the size of pre-existing fly ash particles should be increased, and the temperature drop rate of combustion gas should be kept low.