This report proposes a methodology to solve the inventory routing problem of industrial gases with stochastic demand. The gas tanker distributes gases from a depot to several dispersed customers in a route, and each customer has stochastic demand modeled by a Brownian motion. The proposed model determines the optimal quantity required to refill each customer by minimizing the cost associated with earliness, which increases number of visits per year, and lateness, which increases probability of stockout. Overall, the proposed model minimizes the total system cost, helps find the optimal tanker capacity for a given route, and improves supplier and customers' relationship. Numerical examples and sensitivity analysis are given to illustrate the proposed model.