Abstract: A key requisite for establishing the erosion depth model of the AWJ is to determine the velocities of particles in the outer flow field of the nozzle.In this paper, based on the theory of solid-liquid two-phase flow, a theoretical analysis for particle velocities within an AWJ is presented and the associated particle velocity models are developed.The velocity model is solved by the displacement division method and iterative algorithm.The developed models are finally verified by that the average percentage error between the model value and the corresponding experimental results of PIV is less than 5%.Using the velocity model, the law of movement of particles in the external field of nozzle of AWJ is obtained:① There exists a flow expansion in the structure of the particle flow.② When the particles move along the axial direction of the jet, most of them have experienced a process of acceleration and deceleration.The difference is that they have different acceleration distances.③ On the cross section of the same axial distance in the initial segment, the particle velocity is the same in the potential core.And then the particle velocity decreases gradually along the boundary of the potential core to the jet edge.On the cross section of the same axial distance at the end of the initial segment and the basic segment, the distribution of particle velocity along the radial jet direction fully exhibits a bell shaped distribution.