The scalar generalized-screen method in isotropic media is extended here to transversely isotropic media with a vertical symmetry axis (VTI). Although wave propagation in a transversely isotropic medium is essentially elastic, we use an equivalent “acoustic” system of equations for the qP-waves which we prove to be accurate for both the dispersion relation and the polarization angle in the case of “mild” anisotropy. The enhanced accuracy of the generalized-screen method as compared to the split-step Fourier methods allows the extension to VTI media. The generalized-screen expansion of the one-way propagator follows closely the method used in the isotropic case. The medium is defined in terms of a background and a perturbation. The generalized-screen expansion of the vertical slowness is based upon an expansion of the medium parameters simultaneously into magnitude and smoothness of variation. We cast the theory into numerical algorithms, and assess the accuracy of the generalized-screen method in a particular VTI medium with complex structure (the BP Amoco Valhall model) in which multipathing is significant.