The vector finite element method of tetrahedral elements is used to model 3D electromagnetic wave logging response. The tangential component of the vector field at the mesh edges is used as a degree of freedom to overcome the shortcomings of node-based finite element methods. The algorithm can simulate inhomogeneous media with arbitrary distribution of conductivity and magnetic permeability. The electromagnetic response of well logging tools are studied in dipping bed layers with the borehole and invasion included. In order to simulate realistic logging tools, we take the transmitter antennas consisting of circular wire loops instead of magnetic dipoles. We also investigate the apparent resistivity of inhomogeneous formation for different dip angles.