Soft tissues are one of the human body’s main components. Their constant communication and movements makes their mechanical properties very important to human health. However, soft tissues have complex mechanical characteristics: they undergo large deformations and have non-linear stress-strain relationships. Numerical models in the literature give insight into their behaviour, but most describe the tissues as continuous solids or viscoelastic liquids. In reality, soft tissues have a multiscale organisation, and their microarchitecture is at the origin of their mechanical properties. In particular, the protein collagen, providing the scaffold of the extracellular matrix, is responsible for soft tissue tensile strength, and its organisation directs the tensile properties of mesenchymal-derived soft tissues (connective tissues, bone and muscle). To better describe the link between microarchitecture and macroscopic behaviour, we create a discrete network model using the Growth and Voronoi architectures. Our model replicates some well-known results from the Mikado network literature and expands them to our geometries. These results notably include transitions from a floppy regime to rigidity, and from nonaffine to affine regimes, with the increase of strain, coordination, density and bending rigidity. Additionally, we uncover the role of heterogeneity and micro organisation in the evolution of the network when the value of these latter parameters change beyond what has been done previously. We also extend our model to three dimensions, showing that many of these transitions happen at higher strain and generally that 3D behaviour is softer than 2D behaviour. Further, we also highlight differences, like the apparition of a double strainstiffening with increasing coordination, which is not visible in two dimensions. Together, these results constitute an argument for the mechanical importance of microarchitecture for various collagenous tissues. Moreover, thanks to its computational efficiency and flexibility, our model provides a strong basis for future simulations of collagen gels and soft tissues in two and three dimensions.