The aim of the article is to study the law of distributivity in classical interval arithmetic. We conduct the research for interval in the center-radius form. A set of intervals is represented as a combination of three subsets defined by values relations of centers and the radii. We prove the lemma about conditions under which the sum of two intervals will belong to the same subset of added intervals. The necessary and sufficient conditions for the distributive law hold for the intervals belonging to one of the subsets are offered. We generalize the distributive law in case of voluntary number of intervals. We proved the lemma about the conditions under which the sum of many intervals will own to same subset of the intervals are added. The theorem about necessary and sufficient conditions of generalizing the distributive law for intervals belonging to one subset. These results allow to conduct research to improve the algebraic structure of a set of intervals.
