A model is presented which consists of a dynamical scheme for reproducing the mass hierarchies observed in the quark sector. This is accomplished through new physics beyond the Standard Model, and does not rely upon the Higgs mechanism. By introducing a heavy fermion which couples to the quarks via the emission and reabsorption of a new boson, initially massless quarks are given their masses in a purely radiative fashion. The differences between up and down sector masses appear naturally as a result of generating the down mass matrix from corrections to the up mass matrix: accomplished via an anomalous flavour-changing coupling to the weak sector. Multipole type form-factors are inserted at each coupling, and introduce parameters which are varied to produce numerical fits to the quark masses, mixing angles and CP-violation parameter. Several extensions to the model are proposed and discussed.