The settling velocities of permeable bodies are of interest in fluid-solid reactors, including gas fluidized beds, for example. To better understand this phenomenon, steady flow past permeable cylinders has been investigated both computationally and experimentally. There are two dimensionless parameters in this study: the Reynolds number based on the free-stream fluid velocity and the diameter of the cylinder, and the ratio of the permeability of the cylinder to the square of the cylinder diameter. Using a commercially available computational fluid dynamics (CFD) package, drag coefficients have been computed for flow past a single, permeable cylinder for Reynolds numbers of 10, 100 and 1000, and for permeability ratios ranging from 10\ to 10. In a wind tunnel, drag coefficients have been measured for Reynolds numbers ranging from 800 to 10,000 and for permeability ratios of 1.7;10\ and 6.6;10. In the limit of very low permeability, the computed drag coefficient approaches that for a solid cylinder, as expected. In the limit of very high permeability, the computed drag coefficient asymptotically approaches zero, a phenomenon that can be predicted using D'Arcy's Law. Between these extremes in permeability, however, a distinct dependence of the behavior of the computed drag coefficient on Reynolds number is observed. For higher Reynolds numbers, an increase in drag of up to 50% over that for a solid cylinder has been computed, while for lower Reynolds numbers, very little change in drag is observed. The computational results are in good agreement with experimental results obtained in a wind tunnel; for example, a cylinder with a cross-sectional void fraction of 92.5% was found to have a drag coefficient 42% higher than a similar solid cylinder at a Reynolds number of 1000 (for which the computational results predict an increase of 25%). The computational results are also in general agreement with the limited amount of existing experimental and computational data for permeable spheres.