The paper considers two transport models described using stochastic differential equations system. The investigation is based on a constant function of motion. The approach allows building stochastic dynamical model using a well-known deterministic model and its constant function. The construction algorithm is realized as a software, and it allows choosing a set of functions for simulation. Moreover, it is possible to construct both a system of stochastc differential equations and a system of deterministic ones. The article represents a stochastic model for a vehicle movement and an idea for an itinerant aircraft stochastic model. Transit from a deterministic model to stochastic one is carried out by completing of three addition terms. The first term is a continuous random influence. The second one describes strong random jumps. The third item is an addition component for a drift coefficient. It was shown that choice of additional functions allows building a system of equations with such coefficients that the resolution of this system meets reasonable restrictions. Examples of numerical solutions of the equations constructed confirm the conservation of the value of dynamic invariant under any solution of stochastic differential equations system.