This paper studies full-scale gas neutron tube modeling, including the following processes: gas discharge combustion in a Penning ion source, particle motion in an ion optical system, and modeling the in-target processes, such as sputtering, diffusion, thermal desorption of hydrogen isotopes, and nuclear reactions. Plasma modeling in quadrupole electric and axial magnetic fields was based on the electrostatic particle-in-cell method with molecular kinetic processes. The TechX Vsim software package was used. The neutron tube element sputtering by ions was simulated using SRIM/TRIM software based on Monte–Carlo methods. The OpenFOAM, as an open integrated platform for numerical simulation in continuum mechanics, was used to calculate the hydrogen thermal desorption activated by ion irradiation. The time-dependent neutron yield modeling was performed using the Geant4 software based on Monte–Carlo methods with CHIPS-TPT VNIIA-developed library. In addition, an experimental study of a gas neutron tube with a Penning ion source was conducted here as well. Details are given on the experiment and measurement technique used in this study. The operating characteristics for the gas neutron tube, including amplitude-time characteristics of current flashes (discharge and extraction currents), were determined. The neutron flux dependencies on the discharge current at various accelerating voltages were also obtained. Finally, a comparison between the experimental and calculated results is presented.