Abstract. Based on the relation of order on the set of discrete random variables, which is introduced in the paper, we formalize the arrangement of rectangles with stochastic parameters in a breadth: hit in a breadth, tangency, intersection, non-intersection. We also construct a combinatorial mathematical model of optimal rectangle packing when data are discrete random variables.

Keywords: discrete random variable, combinatorial optimization, linear order, packing models, stochastic optimization, packing of rectangles.