Quantitative analysis of morphological changes in a cell nucleus is important for the understanding of nuclear architecture and its relationship with pathological conditions such as cancer. However, dimensionality of imaging data, together with a great variability of nuclear shapes, presents challenges for 3D morphological analysis. Thus, there is a compelling need for robust 3D nuclear morphometric techniques to carry out population-wide analysis. We propose a new approach that combines modeling, analysis, and interpretation of morphometric characteristics of cell nuclei and nucleoli in 3D. We used robust surface reconstruction that allows accurate approximation of 3D object boundary. Then, we computed geometric morphological measures characterizing the form of cell nuclei and nucleoli. Using these features, we compared over 450 nuclei with about 1,000 nucleoli of epithelial and mesenchymal prostate cancer cells, as well as 1,000 nuclei with over 2,000 nucleoli from serum-starved and proliferating fibroblast cells. Classification of sets of 9 and 15 cells achieved accuracy of 95.4% and 98%, respectively, for prostate cancer cells, and 95% and 98% for fibroblast cells. To our knowledge, this is the first attempt to combine these methods for 3D nuclear shape modeling and morphometry into a highly parallel pipeline workflow for morphometric analysis of thousands of nuclei and nucleoli in 3D.