Flexure of bi-directional functionally graded (FG) circular beams is analyzed using the kinematical assumptions of the Euler–Bernoulli theory. The material properties are varied along the axis (tangential direction) and thickness (radial direction) of the beam simultaneously. Analytical results are presented for statically-determinate circular cantilever beams under the action of various tip loads. Finally, parametric studies are conducted to investigate the variation of critical stresses and displacements with the gradation parameters. These indicate the possibility of tailoring the response of bi-directional FG beams to fit a wide range of structural constraints. © 2016 Elsevier Ltd