While surface waves propagating at tangential discontinuities have been studied in great detail, few studies have been dedicated to the investigation of the nature of waves at contact discontinuities, i.e. plasma discontinuity, where the background magnetic field crosses the interface between two media. In this talk, I will show that, by introducing magnetic field inclination, the frequency of waves is rendered complex, where the imaginary part describes wave attenuation, due to lateral energy leakage. We investigate the eigen-value and initial value problem and determine the conditions of transition from contact to tangential discontinuity. Finally, I will present an investigation into the effect of magnetic field inclination on magnetic Rayleigh-Taylor instability.