This paper deals with forced self-excited vibration accompanied by dry friction, as an example of vibrations of nonlinear systems with discontinuities. The resonance curves of harmonic, higher-hamonic and subharmonic vibrations are obtained using the direct numerical integral method presented previously by us, which is a kind of shooting method and is highly accurate. Chaos and beats are also found. Influences of amplitude and frequency of external force on the stability of solutions are discussed. It is found that bifurcation is realized from the change of the types of vibrations, mamely, change from vibration without stick to that with stick, and vice versa. Periodic solution becomes unstable due to this bifurcation and chaos sometimes occurs abruptly on the halfway through the period doubling route. In this study, a new route to chaos was found using a mechanical model.