Static 1H NMR Free Induction Decay (FID) signals of polymer solids contain a lot of information about the molecular dynamics. A T2 analysis of the FID has generally been performed in terms of discrete two- or three-component models. However, this requires a priori assumption of the number of proton species before analysis. This paper presents a method of analyzing the FIDs of the polymer solid samples in terms of a continuous T2 distribution. A mixed Gaussian and Exponential kernel function was used to represent the true characteristic of FIDs of the polymer solids. A simple and realistic assumption has been made to reduce the number of degrees of freedom in the continuum fitting and to make the fitting stable. An experimental static 1H NMR FID of a typical polymer solid sample was analyzed as an example in the end to demonstrate the application of this method.