This paper deals with integral inventory control in multi-echelon divergent systems with stochastic lead times. The policy considered is an echelon stock, periodic review, order-up-to (R, S) policy. A computational method is derived to obtain the order-up-to level and the allocation fractions required to achieve given target fill rates. Extensive numerical experimentation shows that the accuracy of our approximate method is satisfactory. Further we show that variation in the lead times may have a significant effect on the stock levels required to achieve given target fill rates, hence this variation may not be ignored. Also, it appears that the correlation structure in the lead times may have a significant impact as well.