To validate a particle trajectory model as a first check, one usually applies the model in simulating the dispersion of fine particles in homogeneous and stationary turbulence and compared the simulation results with the classical result of Taylor＇s theory. In this paper we present an analytic procedure to derive the dispersion properties of fine particles in homogeneous and stationary turbulence according to the mechanisms of particle trajectory models. Our approach avoids the use of numerical integration and the finite number of Monte-Carlo trials. This can shed light on the model properties without the mask of errors originated From numerical integration and statistical trials. Based on our approach, nine particle trajectory models in the literature are examined. In addition, the effects of the rime interval of numerical integration taken in the models are analyzed and discussed.