The interaction of vortex rings with thin wire mesh screens is investigated using laser-induced fluorescence (LIF) and molecular tagging velocimetry (MTV). The existence of vortex shedding from individual wires of the porous screens, suggested by prior works, is shown and compared to flow visualization results. A range of interaction Reynolds numbers and screen porosities are studied to determine the conditions affecting the interaction. Transmitted vortex (TV) ring formation is shown to be a function of vortex shedding and the shedding Reynolds number, but not a function of porosity. Screen porosity is shown to affect the TV convective speed but did not impact the formation behaviors. Three major flow regimes existed for the interaction: TV formation with no vortex shedding, TV formation with visible vortex shedding, and no downstream formation with strong shed vortices.