A non-linear analysis of the temporal evolution of finite, two-dimensional disturbances is conducted for plane Poiseuille and Couette flows of viscoelastic fluids. A fully-spectral method of solution is used with a stream-function formulation of the problem. The upper-convected Maxwell (UCM), Oldroyd-B and Giesekus models are considered. The bifurcation of solutions for increasing elasticity is investigated both in the high and low Reynolds number regimes. The transition mechanism is discussed in terms of both the transient linear growth of misfit disturbances due to non-normality, and their possible saturation into finite-amplitude periodic solutions due to non-linear effects.