The static properties of leaves with parallel venation from terrestrial orchids of the genus Epipactis were modelled as coupled elastic rods using the geometrically exact Cosserat theory and the resulting boundary-value problem was solved numerically using a method from Shampine, Muir and Xu. The response of the leaf structure to the applied force was obtained from preliminary measurements. These measurements allowed the Young’s modulus of the Epipactis leaves to be determined. The appearance of wrinkles and undulation characteristics for some leaves (...) has been attributed to the small torsional stiffness of the leaf edges. (shrink)