Many applications, especially in the medical field, need the use of highly deformable membranes with required anisotropic properties. The present work is a contribution towards the processing, characterisation and modelling of anisotropic hyperelastic membranes. An unfilled silicone rubber with perfect hyperelastic behaviour is used. The anisotropy is generated by adding orientated crenels on the upper and lower surfaces of thin membranes during their elaboration. The influence of the relative orientation of the crenels on the mechanical response is characterised by performing tensile tests combined with kinematic field measurements by Digital Image Correlation. Two modellings are proposed. First, a simple analytical equivalent membrane model is proposed aiming to represent the behaviour of the architectured silicone membranes without any more parameter than those used in the hyperelastic constitutive equation of the silicone rubber. Second, the effective properties of the membranes are obtained by an a homogenisation approach with multiple scale asymptotic expansions written in the framework of hyperelasticity and by solving localisation problems on Representative Elementary Volumes with a finite element software. Finally, the experimental results are compared with predictions of two modelling, both approaches are equally efficient to describe them.