||Estimation of elastic parameters of porous rock like the compressibility of sandstone is scientifically important and yet an open issue. This study illustrates the estimation of the elastic compressibility of sandstone (ECS) based on the assumption that the ECS is determined closely by the mineral composition and microstructures. In this study, 37 samples are collected to evaluate the estimations of the ECS obtained by different methods. The regression analysis is first implemented using the 37 samples. The results show that ECS exhibits linear relations with the rock minerals, pores, and applied compressive stress. Then the support vector machine (SVM) optimized by the particle swarm optimization algorithm (PSO) is examined to generate estimations of the ECS based on the mineral composition and microstructures. The SVM is trained with 30 samples to search for optimal parameters using the PSO, and thus the estimation model is established. Afterwards, this model is validated to give predictions of the left 7 samples. By comparison with the regression methods, the proposed strategy, that is, the PSO optimized SVM, performs much better on the training samples and shows a good capability in generating estimations of the ECS of the 7 testing samples based on the mineral composition and microstructures.