Based on the finite element software ANSYS, an electromechanical impedance (EMI) model for a cracked beam with imperfectly bonded piezoelectric patches is established in the paper. The property of bonding layer between the PZT sensor/actuators and the host beam is taken into account and thus the three-dimensional (3D) model of piezoelectric patch-adhesive-cracked beam coupled system is developed. Comparison with existing numerical results validates the effectiveness and accuracy of the present analysis. Then, parameter study is conducted by considering effects of the vibration mode of the host beam, the mass density of the adhesive and crack depth etc. on EMI signatures. The numerical results indicate that the present EMI model can be used to detect the cracks in the structures.