The oscillations of elastic strings and rigid rods in a fluid undergoing uniform shearing motion are considered. It is shown that the oscillations can become unbounded, in the sense of the linearized analysis, when a parameter designated as the shear frequency exceeds the unaffected natural frequency. With the above theory founding the basis of qualitative considerations, an empirical quasi-static analysis is devised for a more realistic situation analoging the wake-induced oscillations of high voltage transmission line bundles. An empirical equivalent of the shear frequency is derived from the analysis. This latter expression has an advantage in the sense of being a simple criterion and requiring only one piece of empirical information, the maximum static lift coefficient. The results are compared with experiments conducted in a wind tunnel using two in-line cables with the leeward cable in the wake of the windward cable. Self-induced oscillations leading to galloping are observed above a critical velocity calculated from the shear frequency criterion.