The pseudospectral methods, especial Fourier method and Chebyshev method are introduced first. Then the first order 2-D elastodynamic seismic wavefield equation based on velocity-stress by the Chebyshev pseudospectral method is solved, and in the compatation the Lame problem, the problem of demolition source in center of homogeneous media, the velocity anomaly intermedia, and the more important problem, headwave propagation in multi-layered media are simulated. At last, we try to get a similar pseudospectral method to Chebyshev method.