A number of calculations have been carried out to determine the currents and fields within superconductors in cylindrical geometry using the critical state model, where the current is assumed field dependent. The calculations were carried out assuming the superconductor to be in the remnant state, i.e. the external field was applied such that the superconductor was fully penetrated in the mixed state, after which the external field was reduced to zero. The aspect ratio of the conductor was varied from the short cylinder to the thin-disc limit. The validity of the two-parameter model of Chen et al has been examined and compared with the Bean model and the calculations are presented in this paper. A relation between the critical current density of the Bean model and the two-parameter model is obtained. Further, a procedure by which the critical current density can be determined in terms of the Kim et al model is outlined. The three models are all in good agreement with experimental magnetic field profiles obtained near superconducting short cylinders.