Accurate identification of sandstone lithology is crucial in resource exploration, geological engineering, and building material research. Hyperspectral is an emerging analytical method with the advantages of spectral integration, a large amount of information, fast analysis speed, and non-destructive testing. It overcomes the problems of long time and complex procedures of traditional analytical methods. The support vector machine (SVM) method has strong learning and generalization ability, and is a fast and accurate analysis method. Therefore, hyperspectral analysis combined with support vector machine modeling established the identification method of different lithological sandstones. Four types of sandstone samples with different lithologies were collected, and their hyperspectral data were collected. Hyperspectral data were preprocessed by standard normal variable transformation (SNV), multiple scattering correction (MSC), and Savitzky-Golay smoothing method (SG), respectively. After that, partial least squares discriminant analysis (PLS-DA) and SVM methods were used to establish classification models. In the SVM model, the Gaussian kernel function (RBF kernel) is selected to establish the SVM classification model. The grid search method optimizes the penalty parameter C and the kernel function gamma parameter in the SVM. The value of C is determined to be (0.1, 1, 10, 100), and the radial basis function gamma parameter is (0.01, 0.1, 1, 10). 16 parameter combinations are formed, and the classification models are established respectively. The five-fold cross-validation classification accuracy of the best PLSDA and SVM models reaches 93.20% and 96.40%. The best MSC-PLSDA and SNV-SVM models established can accurately identify the test set samples. The classification accuracy of the test set of the MSC-PLSDA model reaches 89.00%, and the corresponding F1 values reach more than 80%. The classification accuracy of the test set of the MSC-SVM model reaches 96%, and the corresponding F1 value of the model reaches more than 90%. Among them, the recognition accuracy of argillaceous and fine-grained sandstone is the highest, and the F1 value reaches 100%. The results show that hyperspectral technology combined with the support vector machine method is a reliable method for sandstone lithology identification and analysis, and the spectral preprocessing method has a significant impact on the identification accuracy, which provides a new idea for sandstone lithology identification and analysis systems.