There are many efficient numerical methods for option pricing. Recently, some new numerical integration methods based on Fourier transforms are proposed, such as, the convolution (CONV) method presented by Lord et al (2008, [28]), the fast Hilbert transform approach considered by Feng and Linetsky (2008, [20]), the quadrature (QUAD) method introduced by Andricopoulos et al (2003, [1]), and the cosine (COS) method proposed by Fang and Oosterlee (2008, [18]), etc.. In this thesis, the COS method and the CONV method are applied to price Bermudan barrier options in which the pre-specified monitored dates are many times more than the pre-specified exercise dates. The corresponding numerical algorithms will be presented for practical option pricing. These algorithms work very well and efficiently for different exponential L´evy asset models. Numerical experiments via these algorithms are also given to support the efficiency.