Fibre composite materials are known for their excellent strength-to-weight ratios, making them highly desirable in various engineering applications. The macro-scale behaviour of these fibre composites is heavily influenced by characteristics of the mesoscale, making direct mesoscale modelling crucial for gaining insights. Here, the \textit{mesoscale} refers to modelling individual fibre fillaments as homogenised bundles within a matrix material. The employment of mesoscale modeling methods to assess and predict the behaviour of fibre composite materials has attracted a lot of reaserch the last decades. The current contribution focuses on the challenges and solutions associated with modelling the mesoscale level using state of the art computational techniques. A significant challenge in mesoscale modelling of fibre composites, is generating high quality finite element discretisations. Traditional meshing techniques often fall short, particularly for the matrix component of the structures. The close proximity of fibre bundles creates narrow regions where a high density of elements is required, posing difficulties for meshing software to generate high-quality finite element meshes. To address these issues, our research explores the use of the Finite Cell Method~\cite{Jamshid2007} (FCM), a popular approach within a class of immersed methods. The cornerstone of FCM and immersed methods is the application of straightforward, un-fitted meshes (resembling voxel structures) for discretizing unknown fields, while capturing the geometry through specially designed quadrature rules. This method automates the the discretization process, making it flexible and effective for complex geometries. The proposed methodology is demonstrated on various mesoscale structures of common fibre composite architectures, where its strengths and weaknesses will be highlighted.