Physical parameters of 12 co-compost cover materials were experimentally determined and predicted variations in airflow characteristics were evaluated under varying moisture contents. Predicted air-filled porosity showed high correlation with measured air-filled porosity, facilitating development of a reliable model of air-filled porosity that makes it possible to predict the effect of varying moisture content and compost bed height on air-filled porosity and permeability. Predicted air-filled porosity decreased with increasing moisture content and compost depth for all materials. Air-filled porosity of corn stalks, oat straw, soybean straw, leaves, alfalfa hay, wheat straw, silage, wood shavings and sawdust was in the range of 38–99%. Turkey litter, soil compost blend and beef manure showed air-filled porosity values less than 30% near saturation and the bottom of pile. In concert with the findings of other researchers, effective particle size of all materials increased with increasing moisture content from 20% to 80% of water holding capacity (WHC). It increased dramatically near saturation. In general, permeability increased with increasing air-filled porosity and decreasing bulk density, but the relationship between permeability and moisture content is complex. Permeability is dependent on the balance between particle size and air-filled porosity. If the influence of aggregated particle size on the permeability is significant, it will compensate for the effect of reduced air-filled porosity caused by compaction and moisture content. In this case, permeability will increase; in the reverse case, it will decrease. Permeability decreased for corn stalks, oat straw, silage, wood shavings, soybean straw, sawdust, turkey litter and wheat straw with increasing moisture content from 20% WHC to 50% WHC, regardless of the depth of the compost bed. But the permeability increased with increasing moisture level from 50% to 80% WHC at moderate to shallow simulated bed depths. The soil compost blend and leaves showed the permeability increasing when the moisture increased not only from 50% to 80% WHC but also from 20% to 50% WHC. Permeability of alfalfa hay and beef manure always decreased with increasing moisture levels and pile depth. In this study the maximum wet bulk density and mechanical strength decreased with increasing the moisture content. The method described for determining physical properties under varying moisture contents and compost bed depths will be very useful for designing and modeling airflow characteristics of a mortality composting process with a variety of materials.