Abstract: The κ-ε turbulence model, considering the effect of buoyancy on turbulent kinetic energy and its dissipation rate, is adopted to present a mathematical model for round plumes and jets. There are similarity solutions in the uniform environment. Taking into account the conservation of momentum and heat flux. Finite Analytic Method is applied to obtain the similarity functions of velocity, temperature and turbulent kinetic energy. The agreement between the calculated and experimental data is good.