In the framework of elastostatics, a mathematical treatment is presented for the boundary value problem of the interaction of a flexible cylindrical pile embedded in a transversely isotropic half-space under transverse loadings. Taking the pile region as a stiffened subdomain of an extended half-space, the formulation of the interaction problem is reduced to a Fredholm integral equation of the second kind. The necessary set of Green's functions for the transversely isotropic half-space is obtained by means of a method of potentials. The resulting Green's functions are incorporated into a numerical procedure for the solution of the integral equation. The theoretical response of the pile is presented in terms of bending moment, displacement and slope profiles for a variety of transversely isotropic materials so that the effect of different anisotropy parameters can be meaningfully discussed. Copyright © 2013 John Wiley & Sons, Ltd.