Abstract: The formation out of a borehole is usually radially inhomogeneous due to mud invasion caused by drilling operations.In this study it is assumed that the formation consists of radially multilayered porous layers,and a transfer matrix method is adopted to simulate acoustic well-logging waveforms.It is noticed that the real and imaginary parts of slow compressional wave number are both very large when there is a thick annulus layer out of the borehole at a high frequency,so that the Hankel function is prone to overflow with large arguments.To solve this problem,normalized Hankel functions are introduced to the wave field expressions.The generalized reflection and transmission coefficient method is extended to calculate the wave field in radially multilayered porous formations.Recursive formulae for wave amplitude coefficients are deduced.As an example,acoustic full waveforms are calculated to simulate logging responses in a radially multilayered porous formation with an invaded zone.