The accelerator-driven system (ADS) is an innovative reactor that is being considered as a dedicated high-level-waste burner in a double-strata fuel cycle. (“Double-strata fuel cycle” means a partitioning and transmutation system for long-lived radioactive nuclides.) The target is the physical and functional interface between the accelerator and the subcritical reactor in the ADS, so it is probably the most innovative component of the ADS. Key parameters of ADS are the number of neutrons emitted per incident proton, the neutron multiplicity (n/p), the mean energy deposited in the target for neutrons produced, the neutron energy spectrum, and the spallation product spatial distribution. This paper focuses on the production of neutrons in the spallation reactions. The neutrons produced in the spallation reactions can be characterized by their energy and spatial distributions and multiplicity. The present calculations have been performed using the Monte Carlo code MCNPX. The Monte Carlo simulations have been performed to investigate the neutron multiplicity as a function of incident proton beam energy, as well as a function of target material and target size. Neutron flux distributions at the target surface are calculated and compared with different target materials and proton energies. A comparison of MCNPX with experimental results is made.