During the development of a multicellular organism, a single fertilized cell divides and gives rise to multiple tissues with diverse functions. Tissue morphogenesis goes in hand with molecular and structural changes at the single cell level that result in variations of subcellular mechanical properties. As a consequence, even within the same cell, different organelles and compartments resist differently to mechanical stresses; and mechanotransduction pathways can actively regulate their mechanical properties. The ability of a cell to adapt to the microenvironment of the tissue niche thus is in part due to the ability to sense and respond to mechanical stresses. We recently proposed a new mechanosensation paradigm in which nuclear deformation and positioning enables a cell to gauge the physical 3D environment and endows the cell with a sense of proprioception to decode changes in cell shape. In this article, we describe a new method to measure the forces and material properties that shape the cell nucleus inside living cells, exemplified on adherent cells and mechanically confined cells. The measurements can be performed non-invasively with optical traps inside cells, and the forces are directly accessible through calibration-free detection of light momentum. This allows measuring the mechanics of the nucleus independently from cell surface deformations and allowing dissection of exteroceptive and interoceptive mechanotransduction pathways. Importantly, the trapping experiment can be combined with optical microscopy to investigate the cellular response and subcellular dynamics using fluorescence imaging of the cytoskeleton, calcium ions, or nuclear morphology. The presented method is straightforward to apply, compatible with commercial solutions for force measurements, and can easily be extended to investigate the mechanics of other subcellular compartments, e.g., mitochondria, stress-fibers, and endosomes.