In this study, a set of self-consistency coupled-integral equations for the local magnetic flux and current distributions in a finite superconducting hollow cylinder under an axial magnetic field was directly derived by using the Biot-Savart law and within the framework of the critical-state model. The equations were solved numerically in the three-dimensional space. At the first time, the three-dimensional massive disk problem was solved to confirm the used algorithm and the results were compared with experimental results. In addition to the components of the magnetic flux density and the magnetization, as the hysteresist loops for Bean, Kim and Exponential models were plotted. We assumed that the contribution of the flux penetration from the inner surface of the sample was higher than that of other surfaces. It was found that variation in the area of lateral surface changed the magnitude of the magnetic moment of the finite hollow cylinder in applied magnetic field. The obtained results have a good agreement with authors’ calculations. The formalism presented here can be used for an arbitrary shape of the superconducting system in the presence of any magnetic field dependence of the critical current density J c (B) in an external magnetic field by arbitrary alignment. In addition, a comparison has been made between the magnetic responses of the sample in applying the radial and azimuthal traort currents. It was found that, by increasing of the traort current, saturation value, enclosed area of the hysteresis loops and the initial slopes in the virgin curve decreases. Also we see that, the flux penetration and demagnetizing effect did not affected by the azimuthal angle, the rate of the mentioned changes as the traort current is in azimuthal direction was slower than when that is in the radial direction. In addition, the radial traort current destroyed the azimuthal symmetry of the shielding current distribution and induced the non-uniform magnetic field in the finite sample. The obtained results have shown the importance of the magnetic field dependence of the critical current density on the magnetic response of the finite superconducting hollow cylinder.