Optimization of porous material structures can lead to the design of lightweight foams that can effectively withstand applied loads and mitigate damage. Functionally graded foams have shown several advantages in experimental studies, including tailorable fracture toughness, ability to withstand over 50% strain without a significant decrease in strength and tailorable density. An important aspect of the use of such functionally graded porous media (FGPM) in structural applications is their weight-saving potential. An accurate analysis tool can help in understanding the parameters that will be best suited for a given application. A higher order plate theory is being developed in this work that accounts for extensibility and higher order terms of the transverse rotational strain. The developed theory considers the coupling between principal modes of plate deformation which enables capturing the anisotropic and heterogeneous nature of FGPM. Pores size and shape is assumed to vary through the plate thickness and that being accounted for through homogenization techniques. The accuracy of the theory is being validated against experimental data and existing 3D elasticity solutions. The mechanical response to stimulations was analyzed in the scope of local pore size/shape and overall growth rate through the plate thickness.