A planar silicon carbide/dielectric multilayer structure is investigated in Otto geometry, where surface phonon polaritons and planar waveguide mode can be coupled to realize Fano resonances under transverse magnetic polarization. The resonance coupling is analytically demonstrated using the coupled harmonic oscillator model and numerically presented through rigorous coupled-wave analysis calculations, which shows that the coupling strength between different resonances and the resonant wavelength matching condition plays an important role in the bandwidth and position of the Fano resonance (FR); the magnetic field distribution was also shown to explain the origin of FRs qualitatively.