In many industries, distribution activities are realised in a dynamic environment including uncertainties. Besides, adding transportation mode alternatives, inventory-stocking opportunities in wholesalers, unmet demand permission in distribution centres, etc. increase the difficulty of problem modelling and solving for large-scale networks. In this study, the problem of physical distribution network (DN) design with profit maximisation objective function is modelled to tackle with realistic cases. Two-stage stochastic mixed-integer programming method is used to handle the uncertainties and to consider the probable scenarios. The first-stage decisions of the proposed model are related with the selection of facility location in strategic level, and the second-stage decisions are related with the transported and stocked products or unmet demand quantities. Here, a multi-product, two-echelon, multi-mode and multi-period network model is applied to a hypothetically created problem, inspired from the physical DN of home appliance companies. Various scenarios including stochastic demand and price data with different realisation probabilities are used in the model. The motivation of this study is the lack of reaching a global optimum result using transportation modes as stochastic parameters, considering their own lead times and capacities. Finally, various results are obtained for different cases and analysed in detail.