The propagation of the fast magnetosonic (FMS) wave in the curved magnetic field is studied. A hemicylindrical model of the magnetosphere is considered where the magnetic field lines are represented by concentric circles. An ordinary differential equation is derived describing the coupled Alfv\’en and FMS waves. Using the equation, it was demonstrated that in the curved field the propagation of the fast mode is drastically different from the propagation in the planar magnetic field. In particular, on the magnetic surface known as the reflection surface for the fast mode in the planar magnetic field, there is a wave singularity where some components of the wave’s magnetic field (the azimuthal and compressional components) as well as the plasma density have logarithmic singularity. The physical reason for this singularity is the decrease of the volume of the magnetic flux tube toward the axis of the cylinder.