Guided propagation of whistler waves along cylindrical non-uniformities of a dc magnetic field is studied within the framework of a full-wave approach. Conditions are revealed under which such guiding structures, commonly known as magnetic flux tubes, can support volume and surface eigenmodes in the whistler range. The dispersion properties and field structures of whistler eigenmodes guided by flux tubes with an enhanced magnetic field are calculated and analysed for plasma parameters typical of laboratory experiments. The results obtained are useful in understanding the basic features of whistler wave guidance by magnetic flux tubes and can be applied to interpreting the data of the relevant experiments.