An analytical theory of whistler wave propagation in axially symmetric field-aligned density ducts is developed. Both enhancements and rarefactions of the density (crests and troughs) are considered. Simple equations giving the dependence of the number of modes n upon the angular frequency ω are derived. From these results it follows that in density crests n decreases when ω approaches ω c/2 for ω < ω c/2. The limiting frequency of the wave trapping is calculated. An analytical investigation of wave attenuation in a density crest due to wave leakage is presented. An analysis of the whistler modes in density troughs for ω < ω c/2, ω > ω c/2, and ω → ω c/2 shows that the number of modes is of the same order of magnitude in these three cases.