Any input acceleration that bends RLG dithering axis causes flexure error, which is a source of the noncommutative error that can not be compensated by simply using integrated gyro sensor output. This paper introduces noncommutative error equations that define attitude errors caused by flexure errors. In this paper, flexure error is classified as sensor level error if the sensing axis coincides with the dithering axis and as system level error if the two axes do not coincide. The relationship between gyro output and the rotation vector is introduced and is used to define the coordinate transformation matrix and angular motion. Equations are derived for both sensor level and system level flexure error analysis. These equations show that RLG based INS attitude error caused by flexure is directly proportional to time, amount of input acceleration and the dynamic frequency of the vehicle.