Abstract: Based on the single-backscattering theory of Aki (1969) and the multiple-scattering theory of Gao(1983),a model of single and multiple scattering,with the distance between source and station being not zaro,has been devised in a two dimensional infinite medium. In this model,we considered the effects of single and multiple scattering on coda waves of a heterogeneous medium consisting of uniformly distributed numerous but statistically isotropic scatterers. The power spectral density of coda waves of single and multiple scattering is expressed in analytic form The contributions to the coda power from single and multiple scattering are compared for different distances between the source and station,we obtain the following results: after the direct S-waves,at shorter lapse time,single-scattered waves dominate the earliec parts of the coda,at longer lapse time,the contributions from multiple scattering play an important part in the late parts of the coda waves. And,the longer the distance between source and station,,the earlier the relative time that multiple scattering becomes important.