This work aims at presenting a study using Monte Carlo simulation of a Multileaf Shielding (MLS) System designed to be used for the protection of patients who undergo radiotherapy treatment, against undesired exposure to neutrons produced in the components of the medical linear accelerator heads. The choice of radiotherapy equipment as the subject of study fell on the Varian Clinac 2,100/2,300 with MLC-120 operating at 18 MeV. The general purpose Monte Carlo N-Particle radiation transport code, MCNP5, was used in the computer simulation in order to determine the ambient dose equivalent, H (10), on several points on the patient's plane, with the equipment operation with and without the MLS. The results of the simulations showed a significant neutron dose reduction after the inclusion of the proposed shielding.