This paper describes an algorithm for solving a certain class of bi-criteria multistage transportation problems with transshipment (BMTSP). A several bi-criteria multistage transportation problem with transshipment are formulated. The presented algorithm is mainly based on application of the methods of solving bi-criteria single stage transportation problems, utilizing available decomposition techniques for solving large-scale linear programming problems, and the methods of treating the transshipment problems. The mathematical formulation of the presented class does not affect the special structure of the transshipment problem for each of the individual stages. An illustrative example is introduced to validate that the implementation of the algorithm.