Approximations to the wave motions generated on the surface of an elastic half-space by slip in the vertical mode with friction on a fault plane of arbitrary dip are analyzed. The half-space is initially motionless under uniformly distributed tectonic stresses and hydrostatic stresses due to the weight of the material. The resistance to slip obeys the Coulomb model for static and kinetic friction. Slip is triggered along a line parallel to the fault surface trace. The moving edge of the slip zone extends toward the surface with a constant velocity. Homogeneous function techniques are used to derive the stresses and displacements for a general class of related problems as single integrals of analytic functions. The results are easily specialized to obtain approximate expressions for the wave-induced surface displacement and particle velocity components. For various values of the time, dip angle, coefficient of kinetic friction and rate of extension of the slip-zone edge, curves for the surface particle-velocity components are given. This paper will serve as a basis for future work.