This thesis is concerned with the phenomenon of Rising Damp, which is a complex example of the simultaneous flows of volume (water), heat, solutes and electricity within a porous material. The physical complexity of this natural occurrence has required that the phenomenon be reduced into a series of scientific areas or related topics, which are presented as separate chapters. A full account of the structure of the thesis can be found in the introduction section. The common areas covered in this work are mathematical description of the loss of moisture by damp porous materials (i.e. evaporation) and of the movement of moisture within unsaturated porous materials both in terms of non linear "Diffusivity" type expressions (Chapter Three) or more usefully in terms of non linear "free energy" type expressions (Chapter Eight); capillary suction developed in damp walls. Other less common topics investigated are leaching of soluble materials from the porous matrix and prediction of the consequent increase in matrix permeability to fluid; electro kinetic aspects of Rising Damp; coupling of transport processes within porous materials. Several of the topics discussed in this work are common to several scientific disciplines giving rise to a 'looseness' and 'multiplicity' of nomenclature. To overcome this problem, particular care and space has been devoted to explaining the terminology used in this work, which is especially useful to readers who are unfamiliar with this area of study.To conclude, the thesis covers the essential aspects of Rising Damp and, as such, it may be used as a platform from which the phenomenon can be investigated more comprehensively