Terahertz radiation generation by using the natural modes of solid body has been investigated. The numerical simulation of instability of terahertz range optical phonons in semiconductor structures with quantum wells during the drift of two-dimensional electron gas was performed. The main obstacle of implementing the specified instability is the heating of electron gas during its drift. That is why the investigations were performed for low temperatures T < 77 K, and the electron gas was assumed to be degenerate. Due to the existing closed cycle microcoolers and also the feedback implementation, it is possible to experimentally observe the generation of optical phonons. The numerical simulation involved the use of both kinematic and hydrodynamic approaches. It has been shown that the kinetic approach is more adequate, while the hydrodynamic one leads to overestimated values of instability increments.