The allometric relationship of stem length L with respect to mean stem diameter D was determined for 80 shoots of each of three columnar cactus species (Stenocereus thurberi, Lophocereus schottii, and S. gummosus) to determine whether this relationship accords with that predicted by each of three contending models purporting to describe the mechanical architecture of vertical shoots (i.e., geometric, stress, and elastic similitude, which predict L proportional to D(alpha), with alpha = 1/1, 1/2, and 2/3, respectively). In addition, anatomical, physical, and biomechanical stem properties were measured to determine how the stems of these three species maintain their elastic stability as they increase in size. Reduced major axis regression of L with respect to D showed that alpha = 2.82 ± 0.14 for S. thurberi, 2.32 ± 0.19 for L. schottii, and 4.21 ± 0.31 for S. gummosus. Thus, the scaling exponents for the allometry of L differed significantly from that predicted by each of the three biomechanical models. In contrast, these exponents were similar to that for the allometry previously reported for saguaro. Analyses of biomechanical data derived from bending tests performed on 30 stems selected from each of the three species indicated that the bulk stem tissue stiffness was roughly proportional to L2, while stem flexural rigidity (i.e., the ability to resist a bending force) scaled roughly as L3. Stem length was significantly and positively correlated with the volume fraction of wood, while regression analysis of the pooled data from the three species (i.e., 90 stems) indicated that bulk tissue stiffness scaled roughly as the 5/3-power of the volume fraction of wood in stems. These data were interpreted to indicate that wood served as the major stiffening agent in stems and that this tissue accumulates at a sufficient rate to afford unusually high scaling exponents tot stem length with respect to stem diameter (i.e., disproportionately large increments of stem length with respect to increments in stem diameter). Nevertheless, the safety factor against the elastic failure of stems (computed on the basis of the critical buckling height divided by actual stem length) decreased with increasing stem size tot each species, even though each species maintained an average safety factor equal to two. We speculate that the apparent upper limit to plant height calculated for each species may serve as a biomechanical mechanism for vegetative propagation and the establishment of dense plant colonies by means of extreme stem flexure and ultimate breakage, especially for S. gummosus.