This work presents a new extension to a generalised nonlinear Maxwell model for the theoty of viscoelastic material flow. Nonlinear terms within this constitutive model are used to replicate many experimental phenomena such as shear-thickening/thinning, shear banding and dynamic stress responses found in complex materials such as polymers, Micelles, colloidal dispersions and even granular media. Numerical simulations of the stress tensor under spatially homogeneous plane Couette flow reveal a range of solutions from steady state to chaotic, chosen in part by the strength of nonlinear terms. Bifurcation and stability analysis reveal the onset of chaotic flow and are used to study the various transitions to chaos. A detailed phase space diagram is produced to categorise different dynamical regimes by determining the Lyapunov exponent under variation of two main model parameters. The route to chaos is identified primarily as a Hopf bifurcation.