Following the successes in the fields of vision and language, self-supervised pretraining via masked autoencoding of 3D point set data, or Masked Point Modeling (MPM), has achieved state-of-the-art accuracy in various downstream tasks. However, current MPM methods lack a property essential for 3D point set analysis, namely, invariance against rotation of 3D objects/scenes. Existing MPM methods are thus not necessarily suitable for real-world applications where 3D point sets may have inconsistent orientations. This paper develops, for the first time, a rotation-invariant self-supervised pretraining framework for practical 3D point set analysis. The proposed algorithm, called MaskLRF, learns rotation-invariant and highly generalizable latent features via masked autoencoding of 3D points within Local Reference Frames (LRFs), which are not affected by rotation of 3D point sets. MaskLRF enhances the quality of latent features by integrating feature refinement using relative pose encoding and feature reconstruction using low-level but rich 3D geometry. The efficacy of MaskLRF is validated via extensive experiments on diverse downstream tasks including classification, segmentation, registration, and domain adaptation. The experiments demonstrate that MaskLRF achieves new state-of-the-art accuracies in analyzing 3D point sets having inconsistent orientations. Code will be available at: https://github.com/takahikof/MaskLRF.INDEX TERMS 3D point cloud, deep learning, masked autoencoding, representation learning, selfsupervised pretraining.