A model was formulated to study the behavior of waves in an unstable jet which varied downstream. The linearized barotropic vorticity equation was solved numerically. Waves were forced with a fixed period on the eastern boundary and a radiation condition was applied on the western boundary. In this thesis, cyclic boundary conditions are used on the eastern and western boundaries. The numerical solutions show amplitude growth in time which is approximately exponential. The solutions are normalized and the wave structure is obtained during three time segments. The wave structures are not the same during these segments, but they are very similar in areas of large amplitudes. In these regions the behavior is very similar to that obtained by Tupaz et al. 1978.