In order to investigate a self-excited oscillatory phenomenon of a two-dimensional confined jet with a cylinder as a downstream target, the authors conduct two-dimensional numerical analyses based on vorticity ζ and stream function ψ using a finite-difference discretisation method. At first, confirming the reliability and accuracy of the present analyses, the authors examine two kinds of preliminary tests prior to the main test. Aa a result, the authors reveal (1) the two-dimensionality of the phenomenon by comparing computations with experiments, and (2) the importance and complexity of the upstream of the downstream target.