The study of vibration behaviour of cracked system is an important area of research. In the present work we present a mathematical model to study the effect of inclination, location and size of the crack on the vibrational behavior of beam with different boundary conditions. The model is based on the assumption that the equivalent flexible rigidity of the cracked beam can be written in terms of the flexible rigidity of the uncracked beam, based on the energy approach as proposed by earlier researchers. In the present work the Differential Quadrature Method (DQM) is used to solve equation of motion derived by using Euler's beam theory. The primary interest of the paper is to study the effect of inclined crack on natural frequency. We have also studied the beam vibration with and without vertical edge crack as a special case to validate the model. The DQM results for the natural frequencies of cracked beams agree well with other literature values and ANSYS solutions. © The Authors, published by EDP Sciences, 2017.