MCNP code was used to simulate neutron and prompt gamma ray transport for a range of maze geometrical parameters, wall composition, and wall surface lining. Verification measurements were performed at two medical electron accelerator facilities. A very good agreement was observed between the results of the measurements and the MCNP simulation. MCNP code results were compared with the results of analytical equations used for the calculation of maze effectiveness, derived by Kersey and McCall. A good agreement exists between the simulation results and the results of the analytical methods for maze lengths longer than 8.5 m. However, the results of the present study showed that for shorter maze lengths, Kersey's method tended to overestimate neutron dose at the door entrance, whereas McCall's method with the neutron room scattered correction applied, showed an underestimation of neutron dose. Furthermore, according to MCNP simulation results, the use of barytes concrete instead of standard concrete as room shielding material, reduced neutron dose at the door entrance by about 20%. Finally, it was shown that lining with layers of wood and borated polyethylene significantly reduced the neutron dose at the door entrance by 45% and 65%, respectively.