The propagation of acoustic waves through a fractured one-dimensional medium is examined theoretically with the purpose of determining how the velocity depends on the fracture properties and wave frequency. Wave propagation has been modeled by a modified version of the propagator matrix method. The welded boundary conditions normally assumed for layer interfaces have been replaced by linear slip conditions to represent seismic fracture response. By using a propagator formulation, all intrafracture reflections are included in the calculation of the propagating wave field. Eigenvalue analysis of the propagator matrix allowed for derivation of an analytical solution of the group velocity in fractured rock. Examination of this solution shows that the propagation in fractured rock is strongly dispersive at wavelengths comparable to the fracture spacing. It is also shown how the velocity of a fractured medium is affected by the stiffness and spacing of fractures, at different frequencies. The transition from low to high frequency has been defined by the ratio between the wavelength and fracture spacing. By relating the phase delay between fractures with the phase delay across fractures, it was possible to define an upper limiting frequency for wave propagation. ¿ 2001 American Geophysical Union