We consider an axially symmetric model consisting of radially inhomogeneous horizontal layers. A fast hybrid numerical technique that efficiently combines the integral equations and finite difference methods is applied to simulate the electromagnetic field of an arbitrary source in such models. The boundary value problem is formulated in terms of the electric field components. First, the Green's tensor, which produces zero tangential components of electrical field on the plane boundaries, is calculated in each horizontal layer. Then Green's theorem is used to represent the solution in each layer as a surface integral. Matching the solution on the horizontal boundaries leads to a tridiagonal system of integral equations. The numerical realization of the methods on a finite difference approximation to the initial boundary value the problem in the radial direction and an analytical solution as a function of depth. An eigenvalue problem in the radial direction is solved within each horizontal layer. By matching the solutions at each interface, a tridiagonal system of linear equations is obtained and solved to produce reflection and propagation matrices, which are stored in the computer memory in order to eliminate repetitive calculations when simulating well-logging responses. Several numerical examples demonstrate the high accuracy and efficiency of the method. ¿ American Geophysical Union 1994