A vexing feature in granular materials compaction is density extrema interior to a compacted shape. Such inhomogeneities can lead to weaknesses and loss of dimensional control in ceramic parts, unpredictable dissolution of pharmaceuticals, and undesirable stress concentration in load-bearing soil. As an example, the centerline density in a cylindrical compact often does not decrease monotonically from the pressure source but exhibits local maxima and minima. Two lines of thought in the literature predict, respectively, diffusive and wavelike propagation of stress. Here, a general memory function approach has been formulated that unifies these previous treatments as special cases; by analyzing a convenient intermediate case, the telegrapher's equation, one sees that local density maxima arise via semidiffusive stress “waves” reflecting from the die walls and adding constructively at the centerline.