[en] Highlights: • External circumferential crack problem of superconducting cylinder is investigated. • A functionally graded superconducting cylinder is analyzed. • The magnetically impermeable crack surface condition is applied. • The generalized Irie-Yamafuji critical state model outside the crack region is adopted. - Abstract: In this study, the multiple isoparametric finite element method (MIFEM) is used to investigate external circumferential crack problem of a functionally graded superconducting cylinder subjected to electromagnetic forces. The superconducting cylinder is composed by Bi2223/Ag composite with material parameters varying. A crack reference region is defined to reflect the effects of crack on flux and current densities, and the magnetically impermeable crack surface condition and the generalized Irie–Yamafuji critical state model outside the crack region are adopted. The distributions of magnetic flux density in the superconducting cylinder are obtained analytically for both the zero-field cooling (ZFC) and the field cooling (FC) activation processes. Based on the MIFEM, the stress intensity factors (SIFs) at crack fronts in the process of field ascent and/or descent are then numerically calculated. It is interesting to note from numerical results that for the present crack model in the ZFC activation process, the crack is easily propagate and grow with the applied field increases, and that in the field descent process of either the ZFC case or FC case, the crack generally does not propagate. In addition, in the field ascent process of the ZFC case, the SIFs depend on not only the crack depths and model parameters but also the applied field. The present study should be helpful to the design and application of high-temperature superconductors with external edge cracks.