A novel technique with the potential of detecting hidden fissile materials is presented utilizing the interaction of a single powerful and nanosecond wide neutron pulse with matter. The experimental system is based on a Dense Plasma Focus (DPF) device as a neutron source generating pulses of almost mono-energetic 2.45 MeV and/or 14.0 MeV neutrons, a few nanoseconds in width. Fissile materials, consisting of heavy nuclei, are detected utilizing two signatures: firstly by measuring those secondary fission neutrons which are faster than the elastically scattered 2.45 MeV neutrons of the D-D reaction in the DPF; secondly by measuring the pulses of the slower secondary fission neutrons following the pulse of the fast 14 MeV neutrons from the D-T reaction. In both cases it is important to compare the measured spectrum of the fission neutrons induced by the 2.45 MeV or 14 MeV neutron pulse of the DPF with theoretical spectra obtained by mathematical simulation. Therefore, results of numerical modelling of the proposed system, using the MCNP5 and the FLUKA codes are presented and compared with experimental data.