Fracture zones are pervasive in crystalline areas. When the earth is seen over a sufficiently large volume fracture zones may be too thin to be individually identified. If they have preferred directions in that volume, the volume can be considered to be an azimuthally anisotropic medium.We have formulated the electromagnetic fields induced by a horizontal electric dipole on the surface of a homogeneous half-space with azimuthally anisotropic conductivity. The field components are expressed by the two-dimensional Fourier transform which can be computed by a fast Hankel transform method.The impedance tensor and tipper functions of controlled source tensor magnetotellurics are derived by exciting the dipole source in two different directions. We show the behavior of impedance tensor, tipper functions and their derived quantities: rotational invariants and Parkinson vectors. All transfer functions clearly show anisotropic characteristics. Contours of rotationally invariant apparent resistivities and phases for fixed frequencies are elongated in the direction of maximum conductivity, and Parkinson's vectors tend to point in the same direction.