The aim of the ALICE Collaboration is to study the physics of strongly interacting matter by using the experimental results from a dedicated heavy-ion detector. The Inner Tracking System (ITS) is located at the heart of the ALICE detector surrounding the interaction point. Currently, ALICE is planning to upgrade the ITS for rare probes at low transverse momenta. The new ITS comprises seven layers of silicon pixel sensors on the supporting structure. One goal of the new design is to reduce the material budget (X/X0) per layer to 0.3% for the inner layers and 0.8% for the middle and outer layers. In this work, we perform simulations based on detailed geometrical descriptions of different supporting structures for the inner and outer barrels by using ALIROOT. Our results indicate that it is possible to reduce the material budget of the inner and outer barrels to the expected value. Manufacturing of such prototypes is also possible.