the annular shaped Josephson junction both in an external magnetic field and in a magnetic field generated by the injection current passed along one of the annular junction electrode. However, even in the absence of externally applied magnetic field the Fiske resonances can appear in nonuniform Josephson junctions . Indeed, as was observed in Ref. [14], the randomly distributed barrier inhomogeneities (the structural fluctuations) provide necessary conditions for generation of Fiske steps without external magnetic field. From the experimental point of view the nonuniform Josephson junctions can be formed by including artificial inhomogeneities in the tunnel barrier [15] or by introducing Abrikosov vortices [16, 17]. Inhomogeneities of the first type suppress locally the Josephson tunneling, and, therefore, the spatial variation of Josephson critical current density occurs. These inhomogeneities may be included in the junction barrier during the fabrication process. So a variation of some property of the inhomogeneities (for example, their density) implies necessity to fabricate several Josephson junctions in which this property varies. Obviously, the practical realization of this kind of experiment is a rather complicated task. On the other hand the Abrikosov vortices can be easily trapped in the junction by ap- plying an external magnetic field perpendicular to the junction plane. Moreover, if pinning centers are randomly distributed in superconducting electrodes, the Abrikosov vortices can be trapped in the particular form of a misaligned vortex such that the magnetic field of the vortex enters and leaves the superconducting electrodes of a junction in different points (see Fig. 1). We notice here that an extreme case of misaligned vortices, so called ”pancakes” vortices, naturally appears in high- T$_{c}$ superconductors [18]. The misaligned Abrikosov vor- tices can be considered as local magnetic inhomogeneities leading to an additional spatial variation of the Josephson phase difference ϕ ( ⃗ ρ ), and, hence, the variation of the Josephson critical current density over a junction area [16, 17, 19, 20]. By means of field cooling process one can vary the density of Abrikosov vortices in the same junction. The possibility to trap Abrikosov vortices in a relatively easy way offers many opportunities for experimental stud- ies of Josephson junctions with inhomogeneities. Thus, the dependence of Josephson critical current on the Abrikosov vortices density and an externally applied magnetic field have been intensively studied [16, 17, 19–22] many years ago. Recently, in Refs. [23, 24] a Josephson junction has been used as a tool for monitoring of the position of a single Abrikosov vortex in thermal depinning and Lorentz force depinning experiments. The recent experiments on a spontaneous fluxon formation in annular Josephson junctions demonstrate the necessity to 3