This study deals with the numerical investigation of a chemically reacting methane gas jet which issues into a quiescent atmosphere. Assuming fuel-air mixing to be the rate controlling process (i.e. Infinite chemical kinetics) the Shvab-Zel'dovich formulation has been employed for analysing the turbulent diffusion flame characteristics. A transient FEM scheme in terms of the primitive variables (u, v, p) and the Shvab-Zel'dovich variables β1 and β2 has been implemented for studying the axisymmetric reacting jet problem. The Galerkin's weighted residual approach with 4-noded elements has been adopted for spatial discretization. Numerical predictions for the mixing characteristics of the reacting jet have been carried out for various Reynolds numbers, and results have been obtained for the axial momentum decay, jet spread, and entrained mass flow rate. The axial and radial variations of temperature and mass concentrations of fuel/oxidizer species have been predicted. The variation of flame height with Reynolds number is also obtained. The theoretical results have been validated against the experimental results available in the literature.