Summary: This study deals a two-stage solid transportation problem where on in each stage and each path there are two different capacitated vehicles. As per the quantity of transportation, the larger and/or smaller capacitance vehicles are used. Moreover, the coefficients of the model are assumed bi-fuzzy in nature. The items are breakable in nature and to reduce the breakability rate of the item extra safety cost is introduced here. Finally, the model is justified through a numerical example by using evolutionary genetic algorithm. Also a statistical test illustrates and signifies the feasibility and validity of the proposed model and techniques with a high rate of probability.