In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-