The transmitters of induction well logging tools can be simplified as a series of magnetic dipoles, whose fields formed in dipping boreholes can be decomposed as the sum of transversal electrical and transversal magnetic waves (TE and TM waves), and solved completely from the two scalar partial differential equations. A new process is first given to decompose the electromagnetic field into TE and TM waves through the tensor expression of Maxwell equations in the cylinder system, and then recurrence formula for amplitudes of the field in each bed and generalized reflection and transmission coefficients on each boundary are given. On the bases, the analytic solution of the field in each bed is obtained. Finally, using numerical results, the influence of dipping angles of boreholes, bed thickness and thinly laminated sand/shale on the response of the deep induction well logging tools is investigated.