Cancer invasion is regulated by the interplay between tumour cells and the surrounding extracellular matrix (ECM). The ECM serves a protective role against cancer invasion since it is a physical barrier to be crossed. Yet, it is not a static structure; rather, it constantly undergoes changes that can then favour cancer invasion. Tumour cells modify its structure both by biochemically remodelling and degrading it and by applying mechanical forces. For instance, they can make it stiffer, which in turn favours cell migration. Despite this, the ECM remains a physical barrier to be crossed, but, the conditions leading to tumour cells crossing it are not well understood. Due to the complexity of the cell-ECM system, it is particularly challenging to measure and isolate the effects of the underlying variables. To shed some light, computational modelling has been introduced in the last decades. Nonetheless, so far, computational models have rarely dealt with cells interacting with fibrous networks, as the ECM; instead, they have been focused on considering cells interacting with walls or isolated obstacles. In this work, we introduce a computational framework to model cell migration through fibrous networks. Our model considers two geometric-surface partial differential equations representing the cell (one for the nucleus membrane and the other for the plasma membrane) and a truss structure representing the fibrous network. Although this approach simplifies the cell and the ECM to a minimal representation (two evolving surfaces and a structure of links), it reduces computational efforts while describing the mechanical and biochemical interplay between cells and the ECM. Hence, we can study the role of mechanical and biochemical conditions in hindering or favouring cell migration through fibrous networks.