How cell wall elasticity, plasticity, and time-dependent extension (creep) relate to one another, to plant cell wall structure and to cell growth remain unsettled topics. To examine these issues without the complexities of living tissues, we treated cell-free strips of onion epidermal walls with various enzymes and other agents to assess which polysaccharides bear mechanical forces in-plane and out-of-plane of the cell wall. This information is critical for integrating concepts of wall structure, wall material properties, tissue mechanics and mechanisms of cell growth. With atomic force microscopy we also monitored real-time changes in the wall surface during treatments. Driselase, a potent cocktail of wall-degrading enzymes, removed cellulose microfibrils in superficial lamellae sequentially, layer-by-layer, and softened the wall (reduced its mechanical stiffness), yet did not induce wall loosening (creep). In contrast Cel12A, a bifunctional xyloglucanase/cellulase, induced creep with only subtle changes in wall appearance. Both Driselase and Cel12A increased the tensile compliance, but differently for elastic and plastic components. Homogalacturonan solubilization by pectate lyase and calcium chelation greatly increased the indentation compliance without changing tensile compliances. Acidic buffer induced rapid cell wall creep via endogenous a-expansins, with negligible effects on wall compliances. We conclude that these various wall properties are not tightly coupled and therefore reflect distinctive aspects of wall structure. Cross-lamellate networks of cellulose microfibrils influenced creep and tensile stiffness whereas homogalacturonan influenced indentation mechanics. This information is crucial for constructing realistic molecular models that define how wall mechanics and growth depend on primary cell wall structure.