The dispersion equation governing the guided propagation of TE and TM fast wave modes of a circular cylindrical waveguide loaded by metal vanes positioned symmetrically around the wave-guide axis is derived from the exact solution of a homogeneous boundary value problem for Maxwell's equations. The dispersion equation takes the form of the solvability condition for an infinite system of linear homogeneous algebraic equations. The approximate dispersion equation corresponding to a truncation of the infinite-order coefficient matrix of the infinite system of equations to the coefficient matrix of a finite system of equations of sufficiently high order is solved numerically to obtain the cut-off wave numbers of the various propagating modes. Each cut-off wave number gives rise to a unique dispersion curve in the shape of a hyperbola in the ω-β plane.