In this work a considerable number of papers regarding the cracked beam like structures in the literature are cited. A new and general governing differential equation for eigenvalue analysis of cracked members is derived. Buckling analysis of cracked columns, lateral free vibration of cracked beams, axial free vibration of cracked bars, torsion free vibration of cracked shafts etc. may be considered as special cases. The proposed standard ordinary differential equation is solved and the exact analytical solutions for eigenvalues and mode shapes of these members are determined. Through customizing the general solutions for special conditions the predefined solutions are obtained and the accuracy and robustness of the present study is verified.