Background: Monte Carlo simulations play a vital role in the calculation of the necessary shielding both for neutrons and photons. Advanced and simple shielding materials against neutron and gamma rays were compared by simulation using the MCNB4B Monte Carlo code. The simulations were carried out for the three common neutron sources, namely the ²⁵²Cf, the ²⁴¹Am/Be and the DD neutron generator which are suitable for transportable facilities. Materials and Methods: The source has been simulated as sphere with 3 cm diameter while the necessary shielding is designed in the form of a sphere around the neutron source. The materials considered were chosen according to the EU Directive 2002/95/EC, hence excluding lead and cadmium. Results: In the case of DD neutron generator the thickness, the weight and the volume of the shield can decrease up to 41.3, 44, and 78.4% correspondingly. With regard to the ²⁵²Cf neutron source the use of advanced shielding materials can reduce the corresponding parameters up to 32.7, 40.7, and 68.4% respectively. As regards the ²⁴¹Am/Be neutron source, based on advanced shielding materials the thickness, the mass and the volume of the shield can decrease by 33.8, 49.5, and 70% respectively. Conclusion: The obtained results showed that the use of advanced shielding materials has led to reduce greatly the weight and the volume of the necessary shield.