Problems of the models and IT researches of stochastic periodic flows are considered. The class of periodic piecewise stationary Poisson flows is separated and for one of the versions of this class, when a period of the flow and intervals of stationary process are known, assessment of intensity of the flow is made. For description of the flows with limited aftereffect the interval process is introduced, which allows to consider a function of separation of intervals of the flow. New opportunities of justification of stochastically periodic recurrent flows and flows with limited aftereffect are based on the interval process. As a rule, class of interval periodic processes with uniform distribution is introduced, which is a model of recurrent stochastically periodic flows. Obtained results are the basis of the development of the methods of simulating and statistical analysis of stochastically periodic flows (Poisson, recurrent, etc.)