Guadua angustifolia is a species of bamboo exhibiting excellent mechanical properties in the axial direction, which have been extensively investigated. Few studies have measured other anisotropic constants, which are necessary for reliable theoretical analyses. A simple new protocol is proposed to determine the circumferential–axial shear modulus and axial Young's modulus of this bamboo species by loading slats under torsion and bending. Different theoretical formulations were considered to correlate with the experimental data. The circumferential–axial shear modulus was determined using a torsion formula of strength of materials and an orthotropic finite-element model. The axial Young's modulus obtained using the strength of materials formula was higher than those determined using finite-element orthotropic, isotropic and functionally graded models. The shear and axial moduli obtained with the strength of materials formulae provided relatively good estimates of beam deflections. This protocol can be applied to assess the mechanical properties of other species of bamboo and wood used in structural engineering practice.