Experimental and theoretical studies on material-gap membrane distillation (MGMD) and water-gap membrane distillation (WGMD) are presented in this paper to demonstrate the effect of gaps filled with different materials on permeation flux. A flat-sheet composite membrane composed of an active polytetrafluoroethylene layer and a support polypropylene layer was employed in the experiments. Graphite, water, silica gel, and zeolite were used to measure the effects of these materials on permeation flux and thermal resistance. In the experiments and simulations, the size of the material and water gaps was kept constant at 5 mm. The graphite-filled MGMD permeation flux was approximately 11–22% higher than that of the WGMD at inlet feed temperatures in the range of 40–70 °C. However, the permeation flux of MGMD filled with silica gel and zeolite was 17–24% and 18–27% lower than that of WGMD, respectively. At thermal conductivities below 5 W/mK, the permeation flux of the MGMD with a material packing density of 40% was higher than that with a material packing density of 60%. The MGMD permeation flux with a material packing density of 60% was higher than that with a material packing density of 40% above a thermal conductivity of 5 W/mK. Furthermore, the MGMD permeation flux and overall thermal resistance were primarily controlled by the material gap, with materials having thermal conductivities below 30 and 20 W/mK for the bead- and pellet-type materials (i.e., packing densities of 40 and 60%), respectively.