Sandwich structures, which are light but have high strength, are extensively used in automobile, marine and aircraft structures. However, core/facesheet debonding can occur and reduce the stiffness of the structures and hence result in the failure of the structures, whilst affecting the vibration behaviours. Hammer impact tests and finite element simulations were conducted on flat and curved sandwich structures, which were composed of carbon fibre reinforced polymer (CFRP) facesheets and epoxy cores, to analyse how the vibration behaviours were affected by debonding and other factors. The 15°- and 30°-curved structures showed only slight differences in the natural frequencies of bending and torsional modes. However, significant difference in the lateral modes were found as the mode shape merged with torsional movement and hence the natural frequencies increase. Debonding resulted in the reduction in the natural frequencies, an 80 mm debonded region reduced the natural frequency of the flat and 30°-curved structures by 57.0% and 56.6%, respectively. Change of natural frequencies can make a structure resonate and lead to failure, therefore how the debonded regions affect the vibration of sandwich structures is important for applications.