To use high-Tc superconductors for alternating current transport, it is important to evaluate AC losses. The influence of Jc(B) on the self field losses in a superconductive tube fed by a transport current in incomplete penetration is studied for two reasons. First, superconducting power cables have a geometry that resembles a tube and second, for high-temperature superconductors, the variation of Jc(B) is important especially for low magnetic fields like self field. An analytical calculation of the distribution of the magnetic field B(r,t) by using a linearized law Jc(B) is presented. From B(r,t) one deduces J(r,t) and E(r,t) . The analytical expressions of those were used to calculate the analytical instantaneous power p(t). The losses in the superconducting tube are the average value of p(t) . They are numerically calculated and compared with the measurements taken on a sample whose characteristic Jc(B) was previously measured. With the linear model, the calculated losses are closer to the measured losses than for the Bean model, but the Jc(B) identification remains the main problem.