The E-J power law as electric characterization of the HTS material in Finite Element computations has shown good agreement with measurements of field-dependent crtical current density and losses due to transport current. We use this technique to investigate the loss caused by Ac transport current in self-field and in applied AC magnetic field in both elliptical monocore and multicore tapes, where the current is generated by means of a voltage source. The current density is first kept constant and then varied with local magnetic field. Furthermore, the simulations show that the transfer current decreases due to the screening currents induced by the external field.