Metal and ceramic structures are being fabricated by pressureless sintering of compacted powders. As the powdered compacts are sintered, the pore volume fraction, generally referred to as porosity, decreases while the elastic mechanical properties increase. In this investigation, a new relationship is drawn between porosity and the evolution of elastic mechanical properties in pure ceramic and metal specimens. To develop this relationship, disk specimens are prepared from Nickel and Alumina powders, then sintered to different temperatures. The evolution of porosity is then evaluated from density measurements, while the corresponding elastic mechanical properties are measured using the ultrasonic wave propagation technique. These experimental measurements are compared with several different descriptions: (1) a conventional power law formula, (2) a quadratic formula, (3) a numerical micromechanical porosity simulation, and (4) a new empirical formula that combines the effects of evolving particle cohesion on the elastic properties of the matrix material and the reduction of these properties due to porosity. For the Young's modulus, the new empirical formula provides a better description than the alternative formulas. In the case of Poisson's ratio, similar conclusions could be made. However, the Poisson's ratio exhibited a different sensitivity to particle cohesion that was more directly related to the evolution of particle cohesion.