Rhea's magnetospheric interaction is simulated using a three-dimensional, hybrid plasma simulation code, where ions are treated as particles and electrons as a massless, charge-neutralizing fluid. In consistency with Cassini observations, Rhea is modeled as a plasma absorbing obstacle. This leads to the formation of a plasma wake (cavity) behind the moon. We find that this cavity expands with the ion sound speed along the magnetic field lines, resulting in an extended depletion region north and south of the moon, just a few Rhea radii (RRh) downstream. This is a direct consequence of the comparable thermal and bulk plasma velocities at Rhea. Perpendicular to the magnetic field lines the wake's extension is constrained by the magnetic field. A magnetic field compression in the wake and the rarefaction in the wake sides is also observed in our results. This configuration reproduces well the signature in the Cassini magnetometer data, acquired during the close flyby to Rhea on November 2005. Almost all plasma and field parameters show an asymmetric distribution along the plane where the corotational electric field is contained. A diamagnetic current system is found running parallel to the wake boundaries. The presence of this current system shows a direct corelation with the magnetic field configuration downstream of Rhea, while the resulting j×B forces on the ions are responsible for the asymmetric structures seen in the velocity and electric field vector fields in the equatorial plane. As Rhea is one of the many plasma absorbing moons of Saturn, we expect that this case study should be relevant for most lunar-type interactions at Saturn.