Effect of hydrostatic pressures up to 8 GPa on the crystals of Na 2 C 2 O 4 (sp. gr. P2 1 /c) was studied in situ in the diamond anvil cells a) in neon, b) in methanol-ethanol mixture by high-resolution X-ray powder diffraction (synchrotron radiation, l ¼ 0.7 A, MAR345-detector). Below 3.3-3.8 GPa, anisotropic structural distortion was observed, which was similar to, but not identical with that on cooling. At 3.8 GPa, a reversible isosymmetric first-order phase transition without hysteresis occurred. The orientation of the oxalate anions changed at the transition point by a jump, and so did the coordination of the sodium cations by oxygen atoms. Ab initio simulations based on the generalized gradient approximation of density functional theory have reproduced the main features of the structural changes in the crystals of sodium oxalate with increasing pressure. The theoretical pressure for the isosymmetric phase transition is 3.65 GPa, close to the experimental value; in agreement with experiment the transition was predicted to be reversible. Ab initio calculations gave a pronounced hysteresis for this transition, and have also predicted a further isosymmetric phase transition at 10.9 GPa, also with a hysteresis. The role of temperature in the pressure-induced phase transitions in sodium oxalate is discussed.