An analytical investigation is carried out into effects of crack severity and location on vibration characteristics of a continuous non-proportional damped cantilevered beam. The non-proportional damping is introduced into the system through the use of lumped linear damper at free end of the beam. The crack is assumed to be open in all dynamical conditions, and local stiffness at the crack location is obtained through experimental results. Since the damping distribution is not proportional to a linear combination of stiffness and inertia distribution, it leads to complex eigenvalues and eigenfunctions which makes it difficult to have a proper physical interpretation of the eigenfunctions. Considering this, complex natural frequencies and complex time depending mode shapes which occur in conjugate pairs are obtained and the relationship between frequency changes and crack parameters is discussed. It is indicated that the complex natural frequency change is not the same for each mode since it depends on the location and severity of the crack.