To provide an oil composition for shock of automobiles absorber, improved in a cavitation preventing performance, hardly causing decrease in damping force for a long period, and therefore excellent in sustaining the damping force, in compared with those of conventional ones.

This oil composition for automotive shock absorber is obtained by adding an ethylene-propylene copolymer or a styrene-maleate ester copolymer having a weight average molecular weight (Mw) of 60,000-350,000 as a viscosity index improver in an amount of 1-15 wt.% based on the total weight of the composition to an base oil having a kinematic viscosity of 1-45 mm2/s at 40°C.