Abstract Buoyancy-induced convection in a viscoelastic fluid-saturated porous medium was analyzed using an Oldroydiantype constitutive relation. An autonomous system with four differential equations was deduced by applying the truncated Galerkin expansion Abstract Buoyancy-induced convection in a viscoelastic fluid-saturated porous medium was analyzed using an Oldroydiantype constitutive relation. An autonomous system with four differential equations was deduced by applying the truncated Galerkin expansion