Packed beds have a wide range of applications as heat transfer and energy storage devices. Employed as a regenerator, a packed bed is subject to the flow of a heat transfer fluid, which alternately stores and recovers energy from a packing of discrete particles. The flow direction reverses during the addition and removal of energy. The nature of a packing of discrete particles in a container is such that variations in the resistance to flow and in the void fraction occur across the cross section of the packing. Particularly, the region of the bed near the boundary of the container has a markedly reduced resistance to flow. In addition, the wall effect on the packing geometry changes the void fraction in the near-wall region. The purpose of the present study is to quantify the two-dimensional effects of nonuniform void fraction, velocity, and temperature distributions in a packed bed regenerator on the dynamic and steady periodic behavior. A two-dimensional numerical model of the transient response of a packed bed subject to the flow of a heat transfer fluid has been developed and verified through comparison with measured responses. The model includes the effects of nonuniform velocity and porosity in the bed, and the effects of axial and radial thermal dispersion. The results of the present computations are compared with one-dimensional transient periodic results to demonstrate the two-dimensional effects on the transient response of a packed bed regenerator to a step change in fluid temperature. The classical dimensionless parameters, such as reduced length and reduced time, are not sufficient to characterize the two-dimensional transient nature of a packed bed regenerator. This study identifies the range of bed-to-particle-diameter ratios over which the transient response is significantly influenced by the wall effect on void fraction and flow.