The variation of elastic moduli, M, of sintered powder compacts with porosity, p, has been analysed in terms of an equation M = M(o) (1-p)n, where M(o) is the elastic modulus of non-porous material and n is a constant. The variation of ultrasonic velocities has also been described in terms of a similar equation derived from the relations given by physical acoustics theory. It has been shown that the parameter n is related to a stress concentration factor around pores in the material and is dependent on pore geometry and its orientation in the material. The observed variation in moduli and velocities with porosity has been compared with the theoretically predicted values based on self-consistent oblate spheroidal theory.