In this paper, a linear stability analysis is presented for a non-Newtonian liquid jet moving in a streaming inviscid gas through porous media with three-dimensional disturbances. The dispersion relation between the non-dimensional growth rate and the non-dimensional wave number is derived using appropriate boundary conditions, and it is solved numerically via a new technique using Mathematica software. The effects of different parameters on the stability behavior of the system are discussed in detail. The instability behavior of the jet is influenced by the interaction of liquid viscosity, porous medium parameters, and elasticity. It is shown that non-Newtonian liquid jets are more than their Newtonian counterparts, and that Squire's theorem is in general no longer applicable. It is shown also that the elasticity, Reynolds, Weber numbers; gas to liquid density ratio, and the jet velocity have destabilizing effects; while the porosity of porous medium, medium permeability, surface tension, jet viscosity, and the deformation retardation time to stress relaxation time ratio have stabilizing influences. The dynamic viscosity of the gas to the zero shear viscosity of the liquid and the Ohnesorge number are found to have dual roles on the stability of the considered system. Moreover, it is found that the system is more unstable in the presence of porous medium than in its absence.