The total power in an ultrasonic field is frequently assessed by the measurement of the radiation pressure, although the nature of this phenomenon continues to be the subject of some controversy. This thesis presents a theoretical treatment of radiation pressure together with a discussion of the design and evaluation of a radiation pressure balance. The different techniques used for the determination of ultrasonic fields are discussed in Part I. In particular, the various radiation pressure balances described in the current literature are reviewed. Several apparently contradictory definitions for radiation pressure are in current use, and a number of authors have commented on the confusion that exists within the literature. In Part II of this thesis, a unified and simple treatment of radiation pressure is developed, and, for the one-dimensional case, the time-averaged force per unit area on the surface of an obstacle placed in the field is shown to be exactly related (i.e. to all orders of magnitude) to the time-averaged momentum flux of the wave, or equivalently the time-averaged pressure in the field expressed in Lagrangian coordinates. Unlike all previous treatments, which are based on expansions to second order, the result derived here is valid to all orders of approximation. As it is usual to relate the radiation pressure to other field quantities, particularly the energy density, a relation between these two parameters is also derived. In Part III of the thesis, the design and evaluation of a radiation pressure balance is described, with particular emphasis on a realistic assessment of the sources of uncertainty. The various factors considered in the design of the microbalance system and target are discussed, and this is followed by an evaluation of the effects of phenomena such as surface tension, streaming, convection currents and target stability.