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In this paper we present a new model to compute the current density distribution and the AC losses in multiple YBCO coated conductors by means of coupled integral equations implemented in a finite-element (FE) environment. The model considers the superconducting tapes as 1D objects and allows overcoming the problem of the mesh of conductors of large aspect ratio, typical of 2D implementations; as a result, it is also much faster. The interaction between the different conductors is taken into account by means of a coupling of the electromagnetic variables. The magnetic field distribution in the space between the conductors is computed by coupling the 1D model with a standard 2D magnetic model, which uses the computed current density distributions as sources for the magnetic field. Results are compared with those obtained with standard 2D implementations and with experimental results.