In this paper, a numerical prediction is reported involving second‐order closure of a turbulent flow of a vertically burning, lean mixture of premixed combustible gases discharging from a pipe and developing into a turbulent combusting roundjet. Classical closures are used where available. Expressions for the chemical reaction rate term and other unclosed terms related to variable density flow in the Favre‐averaged turbulent transport equations are based on the Bray–Moss–Libby aerothermochemistry for premixed turbulent combustion, extended to variable enthalpy systems. Mixing of hot burned and cool ambient gases and the attendant buoyancy effects are found to be significant physical phenomena in the behavior of such lean premixed combusting jets. Results of the simulation are compared with experimental data of Yoshida [ProceedingsoftheEighteenthInternationalSymposiumonCombustion(The Combustion Institute, Pittsburgh, 1981), p. 931] with which reasonable numerical agreement is obtained. Reasons for discrepancies and possible lines for future research are discussed.