By solving analytically derived characteristic equations, leaky surface waves are found to exist at an interface between a metal material and a uniaxially anisotropic dielectric material with its optic axis falling in the plane of the interface. Both the assumed lossless metal material with negative relative permittivity and the real metal such as silver having an imaginary part in its permittivity are considered to reveal the difference in the solved leakage loss behavior of the leaky modes. Analytical solutions are also confirmed by the finiteelement eigenmode analysis.