Lamb wave dispersion curves are useful for optimizing the inspection scanning distance that can be covered with good sensitivity in many current applications. However, one of the main problems concerning the calculation lies in selecting a numerical method computationally accurate and efficient. In this paper Lamb waves dispersion curves are generated by the Scaled Boundary Finite Element Method, and by the Rayleigh-Lamb equation. For the semi-analytical case, the waveguide cross-section discretization was performed using isoparametric elements and high order spectral elements. The semi-analytical formulations lead to an eigenvalue problem that can be solved efficiently by calculating the couples of wavenumbers and frequencies that guarantee the wave mode propagation, the basis for generating the dispersion curves. These are compared with those obtained from the analytical solution for the symmetric and antisymmetric modes; in both cases, homogeneous plates of constant thickness are considered. Numerical results show good agreement when using a low number of isoparametric elements, or a single spectral element with shape functions of order six for computing the dispersion curves and wave structure. The calculation is given with a low computational effort and the relative variation with respect to the analytical reference values is less than 2%.