An experimental methodology to measure the stiffness of loosely packed powder beds was developed, which had not been possible using previous methods. Experiments were performed on a range of sample powders including polyethylene, rubber, glass, sand, and clay powders. Powders were placed in a vertical, open, cylindrical vessel, and subject to sweep vibration at low accelerations. Base force and acceleration were measured using an impedance head and accelerometer. Apparent mass, defined as a ratio of base force to base acceleration, measured showed a significant peak frequency. The longitudinal elastic modulus of the bed was calculated from the data. For shallow beds in which the wall friction is negligible, the peak frequency is independent of the cross-sectional area of the bed and sweep rate, but dependent on the bed height and acceleration. Data generated by the top-cap method agreed reasonably for cases in which the packing state was not sensitive to external force. A substantial change in elasticity was detected with changes of packing states. Furthermore, the elasticity of packed beds conforms to Kendall's fourth-order relationship with solid volume fraction over a range of packing conditions.