In this study, we use the three-dimensional, physics-based numerical model, SAMI3 (Sami3 is Another Model of the Ionosphere), to self-consistently generate nighttime, electrified, medium-scale traveling ionospheric disturbances (MSTIDs) at midlatitudes. These are the first numerical simulations to use the fundamental, physics-based equations in a full flux tube model for the self-consistent generation of MSTIDs. We show that a random perturbation results in the development of modes consistent with the Perkins instability and that the growth rate of a specified k perturbation agrees well with linear theory. We also present synthetic observations of MSTIDs: total electron content, integrated 630.0 nm airglow emission, E × B drift, and electron density. The modeling results show the signature of the instability in the geomagnetic conjugate hemisphere, which has been previously observed experimentally. The qualitative descriptions of the E × B drift and electron density profiles of the MSTIDs provided by SAMI3 are found to be consistent with experimental studies of MSTIDs found in the literature.