Using the self-consistent-charge density-functional tight-binding (SCC-DFTB) method, we studied the effect of axial stretching on the electrical conductivity and quantum capacitance of hybrid films formed by AB-stacked bilayer graphene and horizontally oriented single-walled carbon nanotubes (SWCNTs) with indices chirality (12,6). The paper discusses several topological models of hybrid graphene/SWCNT(12, 6) films, which differ in the width of the graphene layer in the supercell and in the value of the shift between the graphene layers. It is shown that axial stretching has a different effect on the electrical conductivity and quantum capacity of the hybrid graphene/SWCNT (12, 6) film depending on the width of the graphene layer. For a topological model with a minimum width of the graphene layer (2 hexagons) under a 10% stretching strain, the transformation of bilayer graphene from planar to wave-like structures is characteristic. This transformation is accompanied by the appearance of the effect of anisotropy of electrical conductivity and a sharp decrease in the maximum of quantum capacitance. For a topological model with a graphene layer width of 4 hexagons, axial stretching, on the contrary, leads to a decrease in the effect of anisotropy of electrical conductivity and insignificant changes in the quantum capacitance. Based on the obtained results, the prospects for using hybrid graphene/SWCNT(12, 6) films as a material for creating flexible electrodes of supercapacitors are predicted.