A crack open may lead to the failure because of rupture or leak in the pipeline. In this paper, the dynamic crack opening displacements (CODs) of a partially debonded pipeline subjected to P and SV waves are predicted, and a mathematical model is proposed. The debonded region around the pipeline is modelled as an interface crack with non‐contacting faces. The wave fields in the bonded and debonded areas are expressed by wave function expansion method, and the expanded coefficients are determined by satisfying the boundary conditions with consideration of cracks. The CODs in the debonding area are represented by Chebyshev polynomials. Some examples are illustrated to analyse the CODs under different thicknesses of pipeline and different wave frequencies. In the region of high frequency, the value of CODs is more sensitive to the crack size. The difference between the CODs in the compression direction and shear directions is also examined. Comparison with existing results is given to validate this dynamic model.