The possibility of REBCO Roebel cables to carry a large amount of current in high external magnetic fields makes them suitable for application in future particle accelerator magnets. The physical phenomena related to the initiation and propagation of a quench event in Roebel cables have not yet been fully analyzed. In particular, given the peculiar architecture of these conductors, the features of the current redistribution and normal zone propagation after quench in individual tapes still require experimental and theoretical investigation. In this paper, an innovative quasi-3D electrothermal FEM model is developed to analyze the effect of quench in HTS Roebel cables. The model is based on a reduced dimensionality approach, under the assumption of a negligible thickness of the individual REBCO tapes. While the tapes are meshed in an identical 1-D pattern, the noncontinuous electrical and thermal contacts among them are accounted for as a sources in the corresponding thermal and electrical equations. Notwithstanding these significant assumptions, the main physical aspects involved in the quench initiation and propagation are retained and correctly described by the reduced dimensionality approach. The quench energy and the normal zone propagation velocity are analyzed for different cable configurations.