AbstractWe study the behaviour of a geometrically exact 3D Cosserat continuum model for an asymptotically flat domain. Despite the inherent nonlinearity, the Γ‐limit of a corresponding canonically rescaled problem on a domain with constant thickness can be explicitly calculated. This “membrane” limit exhibits no bending contributions scaling with h 3 (similar to classical approaches) but features a transverse shear resistance scaling with h for strictly positive Cosserat couple modulus μc > 0. This result is physically inacceptable for a zero‐thickness “membrane” limit model. Therefore it is suggested that the physically consistent value of the Cosserat couple modulus μc is zero. In this case, however, the Γ‐limit looses coercivity for the midsurface deformation in H 1,2(ω , ℝ3). For numerical purposes then, a transverse shear resistance can be reintroduced, establishing coercivity. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)