  We give a method to calculate spectra of the square of the Rarita-Schwinger
operator on compact symmetric spaces. According to Weitzenb\"{o}ck formulas,
the operator can be written by the Laplace operator, which is the Casimir
operator on compact symmetric spaces. Then we can obtain the spectra by using
the Freudenthal's formula and branching rules. As examples, we calculate the
spectra on the sphere, the complex projective space, and the quaternionic
projective space.
