Solved protein structures from PDB depict a static picture, but proteins are flexible. We are interested in understanding how they move near the native conformation, or between two given conformations, without resorting to heavy-duty molecular dynamics techniques. Geometric simulations focus on motions of constrained structures behaving much like mechanical devices, without concern for certain forces (such as electrostatic or hydrophobic interactions). The idea is to isolate specific problems (pertaining to maintenance of geometric distance and angle constraints, or to collisions), and develop the mathematical and computational tools for addressing them efficiently. We will describe static flexibility analysis tools pioneered in the FIRST software, first-generation geometric simulation as done in FRODA, and recent methods aiming at speeding them up.