The response of a reticulated, elastomeric foam filled with colloidal silica under dynamic compression is studied. Under compression beyond local strain rates on the order of $1\u2002s\u22121$, the non-Newtonian, colloidal silica-based fluid undergoes dramatic shear thickening and then proceeds to shear thinning. In this regime, the viscosity of the fluid is large enough that the contribution of the foam and the fluid-structure interaction to the stress response of the fluid-filled foam can be neglected. An analytically tractable lubrication model for the stress-strain response of a non-Newtonian fluid-filled, reticulated, elastomeric foam under dynamic compression between two parallel plates at varying instantaneous strain rates is developed. The resulting lubrication model is applicable when the dimension of the foam in the direction of fluid flow (radial) is much greater than that in the direction of loading (axial). The model is found to describe experimental data well for a range of radius to height ratios $(\u223c1\u20134)$ and instantaneous strain rates of the foam ($1\u2002s\u22121$ to $4\xd7102\u2002s\u22121$). The applicability of this model is discussed and the range of instantaneous strain rates of the foam over which it is valid is presented. Furthermore, the utility of this model is discussed with respect to the design and development of energy absorption and blast wave protection equipment.