[en] A number of technological applications of high-temperature superconductors (HTSC) as superconducting power transmission lines, current leads, inductive fault current limiters, magnetic shields and magnetic bearings are based on bulk components such as tubes, rings, rods, plates. The problem of AC loss reduction is a key issue at the development of superconducting devices operating in AC circuits. In a marked deference from low temperature superconductors, HTSC materials possess smooth voltage-current characteristics and very low thermal conductivity. These features can lead to the pronounced difference of the actual AC losses from the values predicted by Bean1s critical state model. We propose the analytical approaches for AC loss evaluation in HTSC that take into account actual voltage-current characteristics and heating due to AC losses. The obtained expressions explain experimentally observed dependencies of AC losses on frequency and amplitude of the magnetic field. Cases of complete and incomplete magnetic field penetration have been distinguished. The AC losses per cycle decrease with increasing frequency in tile case of incomplete penetration, the case relevant to thick slabs and low amplitude magnetic fields. In thin slabs and large magnetic fields, the case of complete penetration, the losses increase with frequency. It has been shown the manner in which the analytical solutions can be applied for various forms of voltage-current characteristics. The simple criteria for neglecting thermal activated flux creep and flux How and ignoring thermal processes are deduced