The thermal instability of electrically conducting Rivlin-Ericksen elastico-viscous fluid in porous medium is considered to include the Hall current in the presence of a vertical magnetic field. For the stationary convection, the Rivlin-Ericksen elastico-viscous fluid behaves like a viscous (Newtonian) fluid. The Hall current and medium permeability are found to have destabilizing effect, whereas the magnetic field has a stabilizing effect on the thermal instability problem for stationary convection. A sufficient condition for the non-existence of overstability is obtained.