Analytical and numerical models are developed to describe the transport and re-distribution of a highly diffusible substance in the tissues of the body, by the processes of blood flow and diffusion. The models are applied to analagous problems involving, in one case, transfer of matter, specifically an inert gas, and in the other, heat. The specific clinical problems investigated are the measurement of skin blood flow by the clearance of a radioactive inert gas, ¹³³Xe, and the temperature distributions produced in tissue during localised hyperthermia in cancer therapy. The models show that significant exchange of both an inert gas and heat can occur; between the blood and tissue, in blood vessels larger than capillaries. Traditional models based on capillary exchange are therefore limited in small regions of tissue and, the implications of this are discussed for both problems. The clearance of ¹³³Xe from the skin, after epicutaneous application, is shown to be dependent on the diffusion properties of the epidermal barrier as well as the blood flow. The technique is therefore considered unsuitable as a method of measuring skin blood flow. The temperature distributions produced during localised hyperthermia are shown to be greatly influenced by blood flow and thermal conduction. In practical situations the interaction between these two processes can produce complex effects. The possible biological effects of the resulting temperature non-uniformities are outlined and the implications for cancer therapy discussed.