Pressure-driven flow in a model of a thin porous medium is investigated using tomographic particle image velocimetry. The solid parts of the porous medium have the shape of vertical cylinders placed on equal interspatial distance from each other. The array of cylinders is confined between two parallel plates, meaning that the permeability is a function of the diameter and height of the cylinders, as well as their interspatial distance. Refractive index matching is applied to enable measurements without optical distortion and a dummy cell is used for the calibration of the measurements. The results reveal that the averaged flow field changes substantially as Reynolds number increases, and that the wakes formed downstream the cylinders contain complex, three-dimensional vortex structures hard to visualize with only planar measurements. An interesting observation is that the time-averaged velocity maximum changes position as Reynolds number increases. For low Reynolds number flow, the maximum is in the middle of the channel, while, for the higher Reynolds numbers investigated, two maxima appear closer to each bounding lower and upper wall.