The paper presents a theoretical development of the equations of motion for the flexural vibrations of a shallow spherical shell of orthotropic material. For symmetrical vibrations, the motion is described by two ordinary sixth‐order differential equations with variable coefficients. Factorization of the sixth‐order operators into second‐order operators is discussed and the details of solution are worked out for the case in which the equations are reduced to those for the isotropic shell. It is shown that equations for the latter case agree exactly with those derived previously by Reissner. A table of calculated frequencies is given along with some experimental results for steel shells.