Endothelial cells respond to both internal and external mechanical stimuli. Forces within the cytoskeleton and cell-substrate interactions regulate their elongation. This study examines the interplay of these forces in cellular alignment using mathematical modelling. In this work, we formulated a coarse-grained active nematic model that accounts for the viscoelastic properties of the actin network, active forces from bundling proteins, actin turnover, interactions between the actin network and the extracellular matrix via focal adhesion complexes, and contrasts between isotropic and bundled nematic actin networks. We investigate low and high-friction substrate regimes. In each regime, the numerical solution of the model reveals the internal mechanism involved in the progression of cell elongation. Initially, within a circular, well-spread cell configuration, a retrograde flow of transverse and radial stress fibres emerges due to a symmetry-breaking phenomenon. These bundles are highly contractile and give rise to anisotropic contractile forces. These contractile anisotropic forces in stress fibres, along with their interaction with the substrate, lead to alignment in the overall cellular morphology. Furthermore, the mathematical model shows that cell elongation is small on soft substrates, but it is pronounced on high-stiffness substrates due to the formation of a large number of focal adhesions. This allows the stress fibres to exert higher anisotropic forces on the cells, creating more pronounced elongation. Our model effectively predicts both the cellular shape and the internal structure of the actin cytoskeleton, showing good qualitative agreement with experimental observations on endothelial cells.