A closing crack causes the dynamic behavior of a vibrating system to be significantly non-linear and, consequently, the appearance of non-linear resonances (that is super- and subharmonic one). The main idea of the proposed procedure of crack location and size estimation is based on the determination of the vibration response non-linearity around the superharmonic resonance of order 2/1 and subharmonic resonance of order 1/2 at different parameters of driving force. First parameter of driving force under investigation is its point of application. It is shown both numerically, with the use of the finite element model of a cracked beam, and experimentally that the level of non-linearity of vibration response at non-linear resonances is strongly dependent not only on the crack size but also on the driving force application point along the cracked beam. Moreover, the abrupt change of the non-linearity of vibration response when driving force is applied close to the crack clearly indicates its location. In such a way the procedure of damage detection is proposed to estimate both the crack size and location in beams. Second parameter is the level of driving force asymmetry. Addition of the static component to the harmonic driving force varies the state of crack making crack more or fully open or closed. As a result the level of non-linearity of vibration response at any non-linear resonance varies from maximal value (in absence of static component) to practically zero value (when the static component of driving force is so large that crack becomes permanently open or closed at vibration). In such a way the presence of crack can be detected without preliminary information on the vibration response of a structure in the intact state.