The evolution characteristics of monopolar vortices in an irrotational annular shear flow were investigated both experimentally and theoretically. The background flow was generated in a rotating tank by an appropriate source–sink configuration, while the monopolar vortex was created by withdrawing fluid for a short time. Dye-visualization studies demonstrated the gradual destruction of the vortex through a process called ‘vortex stripping’, i.e. long filaments of passive tracers were being shed from the edge of the vortex. In contrast to uniform shear flows, these filaments were asymmetrically attached to the vortex core. Furthermore, the vortex was observed to evolve in a quasi-stationary manner until its final indefinite breaking. The asymmetric stripping process could be explained by modelling both the monopolar vortex and the ambient flow simply by point vortices, and by adopting the method of contour kinematics to trace material contours in the velocity field induced by the point vortices. Furthermore, the effect of a continuous spatial vorticity distribution was investigated by applying the contour dynamics technique, in which the vortex is represented by a stack of uniform vorticity patches. The observed vortex evolution could be well captured by this latter approach.