During the propagation in an anisotropic medium, linearly polarized light in general becomes elliptically polarized. One can detect the polarization state of the transmitted light, but not the evolution of the polarization state during the propagation inside the material. We present a mechanical model where this evolution can be observed. The anisotropic medium is modelled by a series of coupled anisotropic oscillators. An oscillator consists of a bead hanging on an elastic string, and is coupled to neighbouring oscillators with stronger springs. When the system is excited in the plane perpendicular to the springs, the trajectories of the oscillating beads indicate the polarization state of the excitation at their respective positions. We analyze the model analytically, numerically and experimentally.