Presented in this thesis are the following theoretical investigations carried out on the non-invasive microwave hyperthermia of malignant tumours in the human body: Fundamental concepts of electromagnetic wave propagation through a biomass and its interaction with it, are discussed. Various types of applicators used for producing hyperthermia in a biomass, are also discussed. Propagation of a uniform plane electromagnetic wave through a human body is investigated for the general case of oblique incidence. Various models used for the human body have been discussed and the planar multilayer model has been chosen for this study. Reflection and transmission coefficients for both the parallel and perpendicular linear polarisations of the wave, have been determined. For normal incidence, power transfer ratio at the muscle has been defined and calculated at 433, 915 and 2450 MHz (ISM frequencies). Efects of skin thickness and also of fat thickness, on the power transfer ratio at muscle, have been studied. Effects of the thickness and dielectric constant of a bolus, and also of the dielectric constant of an initial layer, on the power transfer ratio, have been studied and their optimum values obtained at the ISM frequencies. For microwave hyperthermia, 915 MHz is recommended as the frequency of operation. Steady-state solution of the bioheat transfer equation has been obtained, assuming the biomass to be a semi-infinite homogeneous medium. Effects of various physical parameters on the temperature profile in the biomass, have been studied. Also studied is the effect of the surface temperature on the magnitude, location and the width of the temperature peak attained in the biomass. A method to determine the microwave power and the surface temperature required to produce a prescribed temperature profile in the biomass, has been developed. The transient-state solution of the bioheat transfer equation has been obtained to study the building up of the temperature profile. Procedures for the design of an open-ended rectangular metal waveguide applicator and for estimating the total microwave power requirement to produce hyperthermia in the human body, have been developed. Performance of the applicators employing linear as well as planar arrays of open-ended rectangular metal waveguide antennas, has also been studied. In order to reduce the overall physical size of the applicators, filling up of the feed waveguide with a high dielectric constant but low loss material is suggested. A simple method of obtaining the elements of the array by partitioning a large aperture by using metal walls has been adopted. Calculation of the total microwave power required by various applicators for producing hyperthermia at various depths in a biomas, have been made and a comparison of the performance of various applicators, has been presented.