In this study, the flow patterns of two-phase (air-particle) swirling or non-swirling turbulent jet in a cylindrical duct are calculated by the Lagrangian and Eulerian methods with the k-ε turbulence model. Calculated results are compared with the experimental data measured by a laser Doppler anemometer (LDA). The Eulerian method performs better for smaller particles (dp=30µm). On the other hand, the results calculated by the Lagrangian method agree better with the experimental data and the Eulerian method overpredicts the axial velocity of the particle phase near the centerline of the jet for larger particles (dp=70µm). It is inferred that the overprediction of the Eulerian method is caused by the underprediction of the turbulent dispersion of mass and momentum of the particle phase in the radial direction near the centerline of jet. The turbulent dispersion of the particle strongly depends on the value of kinetic energy of turbulence(k). Thus we compare the distribution of k calculated by the Eulerian method with the one calculated by the Lagrangian method. The value of k near the jet centerline calculated by the Eulerian method is evidently smaller than the one calculated by the Lagrangian method, therefore, it is inferred that the rate of radial dispersion of the particle phase predicted by the Eulerian method is too slow.