A rubber vibration isolator is used as a muffler hanger or muffler mount between a car body and a muffler to hang the latter from the former. The isolator includes a body made of rubber-like elastic material whose damping factor is high, two holes, upper and lower, formed in the center of the body of rubber-like elastic material, and a weight provided between the two holes and supported at opposite sides thereof by rubber-like elastic members. The rubber vibration isolator is advantageous in that coefficients of transfer of vibrations of both high and low frequencies, respectively, are lowered.