The damage localization in structures represents a challenging task of modern research for which no decisive solution has been proposed yet. With the aim of providing a contribution to the field, in this study some properties of the stationary dynamic response of cracked beams subjected to pulsating loads are explored. To this purpose, the Green’s functions of the multi-cracked Timoshenko beam are first presented. The devised solution is grounded on governing equations embedding distributional terms to account for the presence of cracks; their subsequent integration leads to closed-form expressions of the Green’s functions to be particularized according to four boundary conditions only irrespectively of the number of cracks present along the axis of the beam. Then, the presented solution is exploited for damage location purposes. More precisely, by evaluating the stationary response in terms of deflection at any arbitrary station for the different roving positions of two opposite point forces slightly shifted, abrupt changes of the deflections are encountered as they cross each crack. Indeed, the two opposite point loads cause a different response of the beam whether it is located on the left or on the right of each crack, due to applied external pulsating moment. The observed properties could be exploited for damage location properties, with the enticing advantage, with respect to analogous procedures proposed in the literature, of detecting the number of cracks and their location.