In many industrial applications, fibre-reinforced polymers are in contact with rigid surfaces. The contact behaviour of such polymers is both anisotropic and viscoelastic: the polymers exhibit viscoelastic behaviour and the addition of short fibres results in a directionality in the material behaviour of the composite. This work focuses on the contact problem of an orthotropic viscoelastic material in contact with a spherical rigid indenter, in which the radius of the contact area is much larger than the fibre size. A general form of anisotropic behaviour has been considered in order to describe materials with a high degree of anisotropy. By using separation of variables a solution for the quasi-static contact problem for viscoelastic and generally anisotropic materials is obtained by combining the linear theory of viscoelasticity with the Hertz solution for elastic anisotropic materials as derived by Willis. The developed contact model requires nine elastic material parameters in combination with one time dependent material parameter as input, in order to characterise the behaviour of the material. It is shown that the results of the developed model show good agreement with both isotropic and anisotropic materials described in literature. Furthermore, it is shown that ignoring the anisotropy of a viscoelastic material will result in an overestimate of the stiffness of the material.