A new physics-based compact model, which makes it possible to simulate in a unified way the neutrons and protons of cosmic ray-induced SEU cross-sections, including the effects from nuclear reaction products and from direct ionization by low-energy protons, has been proposed and validated. The proposed approach is analytical and based on explicit analytical relationships and approximations with physics-based fitting parameters. GEANT4 or SRIM numerical calculations can be used as an aid to adjust or refine the phenomenological parameters or functions included in the model, taking into account real geometrical configurations and chemical compositions of the devices. In particular, explicit energy dependencies of the soft error cross-sections for protons and neutrons over a wide range of nucleon energies were obtained and validated. The main application areas of the developed model include space physics, accelerator studies high energy physics and nuclear experiments.