Existing in silico models for single cells feature limited representations of cytoskeletal structures that present inhomogeneities in the cytoplasm and contribute substantially to the mechanical behaviour of the cell. Considering these microstructural inhomogeneities is expected to provide more realistic predictions of cellular and subcellular mechanics. Here, we propose a micromechanical hierarchical approach to capture the contribution of actin stress fibres to the mechanical behaviour of a single cell when exposed to substrate stretch.For a cell-specific geometry of a fibroblast with membrane, cytoplasm and nucleus obtained from confocal micrographs, the Mori-Tanaka homogenization method was employed to account for cytoplasmic inhomogeneities and constitutive contribution of actin stress fibres. The homogenization was implemented in finite element models of the fibroblast attached to a planar substrate with 124 focal adhesions. With these models, the strains in cell membrane, cytoplasm and nucleus due to uniaxial substrate stretch of 1.1 were assessed for different stress fibre volume fractions in the cytoplasm of up to 20% and different elastic modulus of the substrate. A considerable decrease of the peak strain with increasing stress fibre content was observed in cytoplasm and nucleus but not the cell membrane, whereas peak strain increased in cytoplasm, nucleus and membrane for increasing elastic modulus of the substrate. With the potential for extension, the developed method and models can contribute to more realistic in silico models of cellular mechanics.