The Multi-Level Bin Packing problem is a generalisation of the widely-known NP-hard Bin Packing problem. This work aims to investigate approaching this problem, as well as a version including Class Constraints, through integer programming. By modelling the problems in two ways: standard, and with a network flow approach. The studying of the performance of these formulations on various instances, provides a greater insight into the possibilities of integer programming for this purpose. Furthermore, evaluating the two approaches gives an initial suggestion for developing effective models for solving the aforementioned problems.