The electromagnetic waves applied on surfaces of materials with high density of free charges induce the generation of plasmonic waves both in volume and surface. Plasmonic waves in metals have been widely studied; also, recently plasmons have been investigated in intrinsic and doped semiconductor materials. In this work, plasmonic waves are simulated in a two-dimensional electron gas. Two-dimensional electron gas may be created at the interfaces between GaAs and AlxGa1-xAs. The plasmons propagation speed depends on Fermi velocity and Fermi vector of the two-dimensional electron gas. The 2D plasmons dispersion relations deviate from light dispersion at all frequencies and does not have an asymptotic character as in three-dimensional electron gas; this allows operating plasmonic devices with speeds much lower than the speed of light. At low frequencies the plasmon wave vector is much smaller than the Fermi vector and the geometric capacitance dominates the quantum capacitance. The propagation of plasmons in channels without gate is studied.