In the scaled boundary finite element method (SBFEM), the analytical nature of the solution in the radial direction allows accurate stress intensity factors (SIFs) to be determined directly from the definition, and hence no special crack-tip treatment, such as refining the crack-tip mesh or using singular elements (needed in the traditional finite element and boundary element methods), is necessary. In addition, anisotropic material behaviour may be handled with ease. These advantages are used in this study, in which a newly-developed Frobenius solution procedure in the frequency domain for solving the governing differential equations of the SBFEM, is applied to model transient dynamic fracture problems. The complex frequency–response functions are first computed using the Frobenius solution procedure. The dynamic stress intensity factors (DSIFs) are then extracted directly from the response functions. This is followed by a fast Fourier transform (FFT) of the transient load and a subsequent inverse FFT to obtain the time history of DSIFs. Benchmark problems with isotropic and anisotropic material behaviour are modelled using the developed frequency-domain approach. Excellent agreement is observed between the results of this study and those in published literature. The effects of the mesh density, the material internal damping coefficient, the maximum frequency and the frequency interval determining the frequency–response functions on the resultant accuracy and the computational cost are also discussed.