This chapter presents the formulation of the general problem of jets, plumes, puffs or thermals (JPPT) using the Lagrangian method based on the works of Chu (1994) and Dehghani (1996). It is based on two sets of parameters—the spreading coefficients and the added mass coefficients. The spreading coefficients are the parameters that characterize the turbulent motion within the dominant eddies. The added mass coefficients on the other hand are to account for the effect of the irrotational motion surrounding the turbulent flow. These parameters are introduced as required by the one-dimensional (along the path) formulation of the problem. A parallel development of the Lagrangian method was made earlier by Cheung (1991) and Lee and Cheung (1990). The model has been extensively validated against basic laboratory data and applied to a variety of practical engineering problems.