Navigating complex extracellular environments requires extensive deformation of cells and their nuclei. Most in vitro systems used to study nuclear deformations impose whole-cell confinement that mimics the physical crowding experienced by cells during 3D migration through tissues. Such systems, however, do not reproduce the types of nuclear deformations expected to occur in cells that line tissues such as endothelial or epithelial cells whose physical confinement stems principally from the topography of their underlying basement membrane. Here, it is shown that endothelial cells and myoblasts cultured on microgroove substrates that mimic the anisotropic topography of the basement membrane exhibit large-scale 3D nuclear deformations, with partial to complete nuclear penetration into the microgrooves. These deformations do not lead to significant DNA damage and are dynamic with nuclei cyclically entering and exiting the microgrooves. Atomic force microscopy measurements show that these deformation cycles are accompanied by transient changes in perinuclear stiffness. Interestingly, nuclear penetration into the grooves is driven principally by cell-substrate adhesion stresses, with a limited need for cytoskeleton-associated forces. Finally, it is demonstrated that myoblasts from laminopathy patients exhibit abnormal nuclear deformations on microgrooves, raising the possibility of using microgroove substrates as a novel functional diagnostic platform for pathologies that involve abnormal nuclear mechanics.