The packing of compressible biochromatographic resins at large scale suffers from a poor understanding of how column packing method, resin properties, and column geometry impact column performance. To improve understanding, we develop and evaluate a one-dimensional, continuum mechanics model of column packing by mechanical compression. We show that the model can quantitatively predict the change in bed height, applied stress, and internal axial porosity profile without adjustable parameters when the modulus and wall friction coefficients are determined independently. The model possesses theoretical relationships for wall support and resin rigidity that should enable it to describe the mechanical compression of any biochromatographic resin for any column diameter. Moreover, this framework could provide a path to analogous models for flow packing and dynamic axial compression.