Pressure drop across chromatography beds employing soft or semirigid media can be a significant problem in the operation of large-scale preparative chromatography columns. The shape or aspect ratio (length/diameter) of a packed bed has a significant effect on column pressure drop due to wall effects, which can result in unexpectedly high pressures in manufacturing. Two types of agarose-based media were packed in chromatography columns at various column aspect ratios, during which pressure drop, bed height, and flow rate were carefully monitored. Compression of the packed beds with increasing flow velocities was observed. An empirical model was developed to correlate pressure drop with the aspect ratio of the packed beds and the superficial velocity. Modeling employed the Blake-Kozeny equation in which empirical relationships were used to predict bed porosity as a function of aspect ratio and flow velocity. Model predictions were in good agreement with observed pressure drops of industrial scale chromatography columns. A protocol was developed to predict compression in industrial chromatography applications by a few laboratory experiments. The protocol is shown to be useful in the development of chromatographic methods and sizing of preparative columns.