The application of the algebraic stress modeling method (ASM) for calculating the flow in a turbulent vertical round jet is described. The ASM method yields algebraic equations for Reynolds stresses [u’(i)u’j] and turbulent heat flux components [u’(i)T’]. Transport equations are solved for the turbulent kinetic energy k, its dissipation rate epsilon and mean square of temperature fluctuations [T’2]. A new version of the model has been used allowing one to account for the effect of normal Reynolds stresses on energy redistribution in the spectrum of turbulent fluctuations. To model these effects, an additional term has been included into the equation for epsilon. A new effective approach to solving the governing system of partial differential equations is suggested based on the introduction of mathematical variables. Examples of numerical calculations are presented which are compared with the available experimental data of other authors. It has been found that they agree satisfactorily with the results of measurements.