A complete ultrasonic nondestructive testing situation involving a transmitting transducer, scattering from a defect and a receiving transducer is modeled. The defect is taken to be a smooth rectangular crack in an otherwise homogeneous, isotropic, elastic solid. The crack may be located close to a free surface. To solve the scattering problem, an integral equation method is employed. Starting from an integral representation of the displacement field an integral equation for the crack opening displacement is derived. To solve the equation, the crack opening displacement is expanded in a conveniently chosen set of functions with the correct square-root behavior at the crack tips. The transmitting probe is modeled by prescribing the traction on the area of contact. To model the receiver an electromechanical reciprocity argument is utilized which determines the change in signal response due to the presence of the defect. Some numerical results for the signal response are presented for various combinations of the relevant parameters (transducer type, frequency, crack location and orientation). The results are compared to previously obtained results for scattering from a strip-like crack. ©2000 American Institute of Physics.