The present work introduces a mathematical model of a cracked pipeline conveying liquid. This model uses governing equation of Euler – Bernoulli beam theory for a pipe conveying liquid. The crack introduced in the model is represented by two identical torsional springs and a sinusoidal excitation force was applied to one of the pipe ends for the purpose of crack detection. The model is solved numerically using MATLAB code bvp4c to solve linear, ordinary fourth order differential equations (boundary value problem) for the detection of the crack position. To group the variables in the dimensionless form, Buckingham Pi-theorem was used. The effects of the dimensionless parameters on crack position were examined. The results show that the value of dimensionless parameters of stiffness at crack and support has considerable effect on crack position. It also shows that the force amplitude and fluid flow properties has no effect on crack position which demonstrates the capacity of using the present technique with small force magnitude to avoid stress-strain problems on the pipeline and any excitation frequency can be used.