The linear multiple transportation problem with proportional quantitative changes consists of N simple transportation problem (steps) which are interconnected by the fact that the places of destination of the (k - 1)-th step simultaneously are starting places of the k-th step ; k = 2,3,…, N. Besides, a t the transition of the (k - 1)-th step to the k-fh step there is admissible a proportional quantitative change of the goods to be transported which may be different a t all places. The given solution method represents a generalization of the u-v-algorithm for the solution of classical transportation problem to a multiple problem. After the analytical formulation of the problem there are formulized some propositions forming the basis for the solution algorithm given a t the end of the paper. I n the following sections the determination of an admissible basic solution, the calculation of the dual variables and the exchange of basic variables are examined in detail.