When a bulk superconductor endures the magnetization process, enormous mechanical stresses are imposed on the bulk, which often leads to cracking. In the present work, we aim to resolve the viscous flux flow velocity υ 0 /w, i.e. υ 0 (because w is a constant) and the stress distribution in a long rectangular slab superconductor for the decreasing external magnetic field (B a ) after zero-field cooling (ZFC) and field cooling (FC) using the Kim model and viscous flux flow equation simultaneously. The viscous flux flow velocity υ 0 /w and the magnetic field B * at which the body forces point away in all of the slab volumes during B a reduction, are determined by both B a and the decreasing rate (db a /dt) of the external magnetic field normalized by the full penetration field B p . In previous studies, υ 0 /w obtained by the Bean model with viscous flux flow is only determined by db a /dt, and the field B * that is derived only from the Kim model is a positive constant when the maximum external magnetic field is chosen. This means that the findings in this paper have more physical contents than the previous results. The field B * <0 can be kept for any value of B a when the rate db a /dt is greater than a certain value. There is an extreme value for any curve of maximum stress changing with decreasing field B a after ZFC if B * 0. The effect of db a /dt on the stress is significant in the cases of both ZFC and FC.

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