Land plants have evolved a large number of growth forms and each plant species has a unique morphology. For many tall plants, main stems serve the function of vertical growth while primary and higher order branches are responsible for lateral growth for greater light interception. Herein we search for a mechanical constant for primary branches. Primary branches were sampled from 40 species of trees and shrubs. Among the species sampled, branch lengths ranged from 1.8 to 12.2 m, weights from 0.056 to 16.6 kg, base diameters from 17 to 150 mm, bending moments from 7.1 to 2,200 N-m, and section moduli from 0.039 to 29.0 × 10−3 m3. Primary branches of all 40 tree and shrub species exhibited relatively constant bending stresses along each branch. Moreover stress values among the 40 species were relatively constant at about 11 MPa (mean = 11.1 MPa [range 5.2–18.9]; standard deviation = 3.3 MPa). Furthermore, primary branches without secondary branches attached (1) had similar bending moment distributions as tapered cantilever beams, (2) exhibited relatively constant slope values of stress versus length among all species (stresses increased linearly with length), and (3) exhibited both relatively constant density and relatively constant taper within each species. We conclude that the relatively constant stress of about 11 MPa of primary branches was due solely to the numbers, weights, and distributions of secondary branches and associated higher order branches along primary branches for the 40 plant species. To our knowledge, this is the first publication that shows a unifying mechanical constant for primary branches of plants.