Understanding the mechanism by which patterned gene activity leads to mechanical deformation of cells and tissues to create complex forms is a major challenge for developmental biology. Plants offer advantages for addressing this problem because their cells do not migrate or rearrange during morphogenesis, which simplifies analysis. We synthesize results from experimental analysis and computational modeling to show how mechanical interactions between cellulose fibers translate through wall, cell, and tissue levels to generate complex plant tissue shapes. Genes can modify mechanical properties and stresses at each level, though the values and pattern of stresses differ from one level to the next. The dynamic cellulose network provides elastic resistance to deformation while allowing growth through fiber sliding, which enables morphogenesis while maintaining mechanical strength.