In this paper we propose a novel out-of-core technique for progressive lossless compression and selective decompression of 3D triangle meshes larger than main memory. Most existing compression methods, in order to optimize compression ratios, only allow sequential decompression. We develop an integrated approach that resolves the issue of so-called prefix dependency to support selective decompression, and in addition enables I/O-efficient compression, while maintaining high compression ratios. Our decompression scheme initially provides a global context of the entire mesh at a coarse resolution, and allows the user to select different regions of interest to further decompress/refine to different levels of details, to facilitate out-of-coremultiresolution rendering for interactive visual inspection. We present experimental results which show that we achieve fast compression/decompression times and low memory footprints, with compression ratios comparable to current out-of-core single resolution methods.