Biobased fibrous insulation materials, such as vegetal wools, which are able to store atmospheric carbon dioxide, have a number of multifunctional properties. Therefore, they are increasingly used in green building fields. This potential is represented more particularly by acoustic and thermal high level performances due to their specific microstructure. In this context, an innovative acoustic and thermal joint modelling approach has been developed. It is based on a micro-macro homogenisation approach with a cylindrical geometry representative of the fibres morphology. The specificity of this approach is based on the energy equivalence between a generic inclusion, representative of the fibrous material physical and geometrical properties at microscopic scale, and the homogeneous equivalent medium at the macroscopic scale. Thus, the equivalent thermal conductivity is determined statically from the coupling of a cylindrical Self-Consistent Method (cylindrical SCM) for conduction transfer with a semi-empirical model for radiation transfer. For the sound absorption coefficient, the macroscopic behaviour laws are established by using the homogenisation of periodic media (HPM). In order to obtain analytical solutions, a HPM-SCM (cylindrical geometry) coupling dynamic model can be used. Validation of both acoustic and thermal models is carried out by comparing results with experimental data. It is thus shown that it is possible to group them together into a joint procedure based on only two input parameters, the fibrous material open porosity and an equivalent fibre radius value.