A relatively slow rate of loading in the low velocity impact problems and confinement of the deformation and damage to the vicinity of the impact area makes the Hertzian theory of elastic contact a useful tool for the analysis of the impact-induced stresses. For instance, Willis' explicit solution to the contact problem for a transversely isotropic half-space, whose axis of material symmetry coincides with the axis of loading (axisymmetric problem)  is directly applicable to the analysis of the contact stresses in quasi-isotropic composites. The in-plane properties of the quasi-isotropic composites are independent of the angular coordinate but different from the through-the-thickness properties. This makes such composites transversely isotropic with respect to the through-the-thickness direction. In contrast to the quasi-isotropic composites, the problem of transverse impact of unidirectional composites and the associated contact problem are three-dimensional, because the axis of the material symmetry, which coincides with the fiber direction, does not align with the axis of the applied impact load. This particular problem provides physical grounds for the present study. In this work a unidirectional fiber reinforced composite subjected to transverse low velocity impact in the direction perpendicular to the fiber direction is considered. A corresponding three-dimensional contact problem and its exact solution are discussed. Stress and strain fields are obtained in the form of contour integrals in the complex plane and calculated for two materials with different ratios of longitudinal and transverse Young moduli. Effect of anisotropy on the stress filed is discussed.