Here are considered composite materials reinforced which strong fibres, which have an important property that they are anisotropic, and in many cases this anisotropy may be very strong, in the sense that mechanical properties are strongly dependent on direction. Such materials are highly resistant to deformation by extension in the fibre direction compared to other deformation modes. Thus material has been modelled as a transversely isotropic for which the extensional modulus in the fibre direction is much greater than that in a direction perpendicular to the fibres. Material is modelled as coordinate free and such model is employed for examination of waves propagating in an infinite plate reinforced by strong fibres. Wave propagation in layer reinforced by one family of fibres with wave direction parallel with stress free boundaries, but otherwise with angle arbitrary to fibre direction, are examined here. The dispersion relations, in specific carbon fibres - epoxy resin composites, are examined. Expressions are also obtained for the variation of displacements and stresses through the thickness of the plate.