There has been increasing experimental evidence of non-affine elastic deformation mechanisms in biological soft tissues. These observations call for novel constitutive models which are able to describe the dominant underlying micro-structural kinematic aspects, in particular relative motion characteristics of fibrous constituents and the implication to oriented material behaviour. This contribution proposes a flexible and modular continuum framework based on a generalised continuum encompassing bulk and fibre constituents, respectively. In addition to the displacement field associated with the bulk material, it features a separate tangent map to independently describe the deformation of the fibres. Accordingly, the non-affine fibre deformation and strain relative to the bulk material including interface stress is readily available to formulate constitutive relations for bulk and fibre materials as well as their mutual interaction. Associated stress quantities are naturally derived from a corresponding generalised variational principle featuring dedicated governing equations for the displacement field and the fibre tangent map. This aspect of the framework is crucial for the truly non-affine kinematics description within the elastic deformation regime. In the context of biological soft tissue modelling, the applicability of the formulation is studied for tension-inflation experiments of carotid arteries [1]. REFERENCES [1] Krasny, W., Magoariec, H., Morin, C. and Avril, S., 2018. Kinematics of collagen fibers in carotid arteries under tension-inflation loading. Journal of the mechanical behavior of biomedical materials, 77, pp.718-726.