We have adapted Pathak's (1979) solution for high-frequency electromagnetic waves scattered by a right circular cylinder to the equivalent SH scattering problem. Previous treatments are valid only in restricted zones of the scattered field. This formulation applies in all zones and smoothly connects the wave field across (1) the deep shadow zone, (2) the penumbra, and (3) the deep illuminated zone. We have developed methods to evaluate Pathak's functions using Taylor's expansion in the penumbra zone, residue theory in the shadow zone, and saddle point integration in the illuminated zone. Results compare well with mode summation values at 1 / 36 computer time. We calculate causal synthetic seismogram sections for scattering of SH pulses from hard and soft cylinders. We find that the 0.5 amplitude position lies within the shadow boundary for a soft scatterer and outside for a hard scatterer, contrary to findings of the Kirchoff theory. We provide diffraction and attenuation coefficients required to solve scattering problems of objects of arbitrary shape, but smooth curvature, using the geometrical theory of diffraction (GTD, Keller, 1956).