This paper discusses the use of singular values and singular vectors in the solution of large inverse problems that arise in the study of physical models for the internal structure of the Earth. In this study, the Earth is discretized into layers and the layers into cells, and travel times of sound waves generated by earthquakes are used to construct the corresponding physical models. The underlying numerical models lead to sparse matrices with dimensions up to 1.3 x 10⁶ - by -3 x 10⁵. Singular values and singular vectors of these matrices are then computed and used in the solution of the associated inverse problems and also to estimate uncertainties. The paper outlines the formulation adopted to model the Earth and the strategy employed to compute singular values and singular vectors, shows results for two models that have been studied, comments on the main computation issues related to the solution of these problems on high performance parallel computers, and discusses future improvements of the adopted computational strategy.