A mathematical formulation is developed for describing the rate-dependent behaviour of transversely isotropic soils. The constitutive relations are derived within the framework of elasto-viscoplasticity and the soil microstructure is defined in terms of a unit vector specifying the preferred material orientation. The formulation is applied to analyse an embankment problem involving the progressive creep of a lightly overconsolidated clay under undrained conditions. This chapter outlines a methodology for modelling the rate-sensitive behaviour of transversely isotropic soil. It aims to derive the constitutive relations within the context of elasto-viscoplasticity, following a framework similar to that described by S. Pietruszczak. The chapter illustrates the framework by a series of examples which examine the sensitivity of material response to the degree of anisotropy. The numerical analysis incorporates a viscoplastic model developed by D. F. E. Stolle et al. for simulating the time-dependent response of Haney clay. The mathematical formulation has been applied to a numerical study involving simulations of the time dependent response of a lightly overconsolidated clay. The chapter describes the elastic as well as viscoplastic properties by incorporating a vector operator which defines the preferred material direction. The numerical analysis confirms the ability of the model to capture the directional effects, i.e. the sensitivity of the stress-strain response, as well as the effective stress paths, to the orientation of the sample.