Abstract: A method and apparatus for measurement of the eccentricity dimension which measures the eccentricity dimension .alpha. between optical fibers and a coating member of a fiber ribbon made up of optical fibers and a coating member having a rigidity relatively lower than the fibers and covering the outer surface of fibers. When taking up the fiber ribbon at a constant speed, the rotational speed .omega..sub.a of a first rotary drum made to contact one surface of the fiber ribbon and the rotational speed .omega..sub.b of a second rotary drum made to contact the other surface of the fiber ribbon are measured and the radii R of the rotary drums, the overall thickness t of the fiber ribbon, and the rotational speeds .omega..sub.a and .omega..sub.b of the rotary drums are substituted in the following equation to compute the eccentricity dimension .alpha.:.alpha.=(.omega..sub.b -.omega..sub.a) (R+t/2) / (.omega..sub.b +.omega..sub.