A novel particulate trajectory model (PTM) is developed to predict axial transport and dispersion of municipal solid wastes (MSW), based on the vector analysis on particle's gravity-induced axial displacement in a single excursion. Three parts of work are extended with respect to this PTM. First, the simplified formulas about mean residence time (MRT) and material volumetric flow (MVF) are derived by incorporating statistic-averaged analysis on all repeated excursions of solids within kiln into PTM. The correctional factors-et for MRT and ef for MVF-are introduced to improve the model's validity under such practical cases, i.e. irregular MSW existence or internal-structure presence. Reasonable agreement is obtained between the empirical formulas and experiments with correlation factor in excess of 90% for all runs. Second, a stochastic PTM is extended to predict the residence time distribution (RTD) curves of segregated MSW by considering the probability of the rolling distance of individual particle. As for MSW, the main cause of axial dispersion is the egregation of rolling distance of solids, due to variation of MSW components, shapes and sizes. Finally, the optimization model for geometry design of a laboratory-scale rotary kiln pyrolyser of MSW is presented and the corresponding optimum solutions are provided.