The stability of natural convection in a vertical layer of heat-generating Darcy porous medium saturated with an Oldroyd-B fluid using a local thermal non-equilibrium (LTNE) model has been investigated numerically. The impermeable vertical walls of the porous layer are maintained at different uniform temperatures. As a consequence of LTNE model, two temperature equations representing the fluid and solid phases separately are used for the heat transport equation. A uniform volumetric heating in both fluid and solid phases is considered and the transfer of heat between the phases is considered in the basic state. The internal heating introduced asymmetry in the basic flow which led to the existence of competing modes. The intricacies of internal heat source strength in the fluid and the solid phases are clearly discerned on the stability of the system. The stress relaxation parameter Lambda(1), fluid-heat generation parameter Q(f), solid-heat generation parameter Q(s) and the porosity-modified conductivities ratio gamma were found to exhibit destabilizing effect on the system, while the strain retardation parameter Lambda(2) shows an opposite trend even in the presence of internal heating.