The demand for good quality drinking water is steadily increasing worldwide. Membrane distillation was introduced in the late 1960-s, but did not yet attain commercial status as a water desalination process, partly because membranes with the characteristics most suitable for the process were not available then, especially at reasonable price. A state of the art critical review included in this dissertation indicated that the approach to modeling MD so far was by assuming the process as onedimensional and applying empirical heat and mass transfer coefficients. Moreover, the scatter in both theoretical and experimental results found in the literature suggested that this process needs better experimental and modeling work. This work advances the state of the art by presenting a transport analysis of air gap membrane distillation (AGMD) and of direct contact membrane distillation (DCMD), based on a two-dimensional conjugate model in which, the temperature and concentration of the hot and cold solutions both normal to the membrane and along it are solved, so that the sensitivity of the permeate flux to the major system parameters could be better evaluated. Employment of spacers in the flow channels for improving the process by reducing the convective resistance is also investigated. Significantly, this is the first comprehensive analysis and exposition of all resistance to heat and mass transfer in the process. The solutions were validated in comparison with available experimental results. The modeling and sensitivity analysis provide useful basic detailed information about the nature of the process, and are helpful for process improvement and optimization. Some of the principal conclusions are: 1) the air/vapor gap has the major role in reducing the parasitic heat loss in the process, (2) the gap width has an important effect: decreasing it 5-fold increases the permeate flux 2.6-fold, but the thermal efficiency improves only slightly because the conductive heat loss increases too, (3) increasing the inlet temperature of the hot solution has a major effect on the permeate flux and also increase the thermal efficiency, while decreasing the coolant temperature has a lesser effect on the flux increase, and even slightly reduces the efficiency, (4) the feedwater salt concentration has a very small effect on the permeate flux and thermal efficiency, (5) the inlet velocities of the hot and cold solutions have a relatively small effect, ( 6) reducing the thermal conductivity of the membrane material improves the process thermal efficiency somewhat, (7) the permeate flux ofDCMD is higher than that of AGMD by about 2.3-fold at Thi= 80 °C and becomes even higher for low inlet saline feedwater temperatures (at Thi= 40 °C, JocMo/hGMD= 4.8), (8) the sensitivity ofDCMD to the main process parameters is more noticeable than that in AGMD, (9) for MD it appears that the central type is the most effective one, and can improve the flux by about 33% over the empty channel.