In the case of existence of an applied magnetic field, the movement of the ring-shape quasi-fluxons in the circular symmetric annular Josephson junctions is investigated numerically. The behavoir of the quasi-fluxons in an applied field depends upon the geometric size of the junctions. If the width of the annular junctions is 5λJ in the radial direction, the life time of the quasi-fluxon is increased by applied field. If the width of the annular junction is 10λJ, the life dme of the quasi-fluxon is increased as well, and in addition, some evident changes of the behavior of the quasi-fluxons occur in the process of propagation and in the reflection at the boundary, due to the applied field. The size of the first zero-field step increases with applied field in the lower current direction. These changes are caused by an inhomo-geous distribution of the applied field in the junctions. A tunable resonator in the gigahertz-range using quasi-fluxons on a lossy large-area annular Josephson junction is also proposed in this paper.