It is well known that the critical current density J c of a superconducting material depends on the magnetic field B. If magnetic independent J c is chosen for analytical calculation of current distribution, the critical current I c corresponds to full penetration current I p. I c is a measured current with 1 μV/cm criterion and I p is a calculated current. The aim of this paper is to calculate the influence of the J c( B) variation on I p of a superconducting tube. To calculate I p, which is depending on the material itself, a linear function J c( B) is sufficient to obtain realistic values by analytic way. We need to have a linear J c( B) law that is close to the measured J c( B) characteristics presented in this paper. The linear J c( B) law chosen was used for the calculation of the distribution of both magnetic field B( r, t) and the current density J( r, t). These distributions allow the analytical calculation of I p. The calculated results of magnetic field distribution and full penetration current with Bean model and linear model are compared. We also present the variation of critical current with the characteristic parameters of the material. The present results, allow to understand the relationship between the full penetration current variation of a sample and the variation of the J c( B) characteristics.