TThe quasi-cylindrical approximation is used to describe numerically the structure of a submerged swirling jet for subcritical values of the swirl ratio S<Sc . The emerging flow structure is affected by the swirling motion, which enhances the entrainment rate of the jet and induces an adverse pressure gradient that reduces its momentum flux. The effect is more pronounced as the swirl ratio S is increased, yielding for sufficiently large values of S a jet with an annular structure. The integration describes the smooth transition towards the far-field self-similar solution for all values of S smaller than a critical value S5Sc , at which the numerical integration fails to converge at a given downstream location. The comparisons with previous experimental results confirm the correspondence between the onset of vortex breakdown and the failure of the quasi-cylindrical approximation.