Using the framework of the chromodielectric model we perform an analysis of color electric flux tubes in mesonlike q q and baryonlike qqq quark configurations. We discuss the Abelian color structure of the model and point out a symmetry in color space as a remnant of the SU(3) symmetry of QCD. The generic features of the model are discussed by varying the model parameters. We fix these parameters by reproducing the string tension 980 MeV=fm and the transverse width 0:35 fm of the q q flux tube obtained in lattice calculations. We use a bag constant B 1=4 240 ÿ 260 MeV, a glueball mass m g 1000 ÿ 1700 MeV, and a strong coupling constant C F s 0:2 ÿ 0:3. We show that the asymptotic string profile of an infinitely long flux tube is already reached for q q separations R 1:0 fm. A connection to the dual color superconductor is made by extracting a magnetic current from the model equations and a qualitative agreement between the two descriptions of confinement is shown. In the study of the qqq system we observe a -like geometry for the color electric fields and a Y-like geometry in the scalar fields both in the energy density distribution and in the corresponding potentials. The resulting total qqq potential is described neither by the -picture nor by the Y-picture alone.