Living adherent cells change their orientation in response to substrate stretching such that their cytoskeletal components reorganize in a new direction. To study this phenomenon, we model the cytoskeleton as a planar system of elastic cables and struts both pinned at their end-points to a flat flexible substrate. Tensed (pre-strained) cables represent actin stress fibers, whereas compression-bearing struts represent micro-tubules. We assume that in response to uniaxial substrate stretching the model reorients and deforms into a new configuration that minimizes its total potential energy. Using the Maxwell's global stability criterion, we find global minima configurations during static extension and compression of the substrate. Based on these results, we predict reorientation during cyclic stretching of the substrate. We find that in response to cyclic stretching cells either reorient transversely to the direction of stretching, or exhibit multiple configurations symmetrically distributed relative to the direction of stretching. These predictions are consistent with experimental data on living cells from the literature.