Using a realizable non-linear κ-ε model, the approximate solutions are derived for the fundamental properties of a swirl jet. The functional forms of velocities and κ-ε distributions are assumed as a first approximation. The unknown coefficients in the functional forms are obtained as the functions of the non-linear κ-ε model constants by substituting the assumed mathematical expressions into the continuity, momentum and non-linear κ-ε equations. The coefficient of eddy viscosity (=cμ) is determined as a function of strain and rotation parameters to satisfy the realizability. Approximate solutions for the turbulent properties are derived from the non-linear Reynolds stress equation. Neglecting the swirl parameter, the same solution is applied to a round jet without swirl. A well agreed comparison is attained between approximate solutions and previous experimental results.