Summary: The paper presents a stochastic method for estimating of the position of marked particles in a river reservoir, if they appear at the beginning of backwater at the time-point \(t=0\). Particles are assumed to be in water solution. The stochastic method is used because of the complexity of the reservoir geometry and flow conditions which cannot be simply described mathematically. The resulting expression (for the present in one horizontal layer only) defines the area outside of which the particles, after a time interval (0,t), will appear with a given small probability. The practical consequence of presented theoretical results is in the formulation of coefficients (i.e. the variances of path lengths which particles attain in the above mentioned time interval) which must be measured in analogical field conditions to quantify the results.