The generation of photoneutrons in ultra-intense short laser-solid interactions is modeled, and the properties of the laser-induced photoneutron sources are studied using the Monte Carlo simulation code Fluka. Further, neutron generation is simulated for different materials and electron temperatures. The results denote that tungsten exhibits the optimal performance and that the neutron yield exhibits different saturation thickness values at different temperatures. The neutron source size can be determined using the electrons'' spread angle and the target thickness. Ratios that are as high as 5 can be achieved between the fluxes in the forward and sideways directions by increasing the target radius. Further, stable energy spectra can be obtained for the photoneutron source when the electron temperature is greater than 4 MeV. The time distribution results denote that the neutron pulse duration is less than 30 ps and that its stretching factor after flight is 100 ps/mm.