In this paper, the effect of the crack on the vibration behavior of a thick-walled cracked pipe conveying fluid is investigated. The presence of a crack on the pipe introduces considerable local flexibility at the crack location. This flexibility is modeled by the fracture mechanics approach. The accuracy of the model is validated through the experimental data reported in the literature. Then, by using the mentioned model, the vibration analysis of the cracked pipe conveying fluid has been accomplished. Moreover, in order to solve the equation governing the vibration of the cracked pipe conveying fluid, a new analytical technique based on the power series method is proposed. Then, by applying the boundary conditions and the compatibility conditions at the crack location, the frequency equation is obtained. The results are presented by appropriate curves showing the variation of the natural frequency of the cracked pipe conveying fluid in terms of the crack depth and the fluid flow velocity. Also, the results show that for a cracked pipe with a given depth and location for the crack, by increasing the fluid flow velocity, the natural frequencies of the pipe decrease. Also, as the fluid velocity approaches to a certain value, the fundamental natural frequency approaches zero and instability occurs.