An analysis is presented for the free vibration of circular‐segment‐shaped membranes and plates of rectangular orthotropy. A circular‐segment‐shaped membrane is formed on an orthotropic rectangular membrane by fixing several segments. With the reaction forces acting on the edges of an actual membrane regarded as unknown harmonic loads, the stationary response of the membrane to these loads is expressed by the use of the Green’s function. The force distribution along the edges is expanded into Fourier series with unknown coefficients, and the homogeneous equations for the coefficients are derived by restraint conditions on the edges. For a circular‐segment‐shaped plate clamped at the edges, it is formed on a rectangular plate simply supported at the edges, in which the bending moments act on the edges in addition to the reaction forces. In this case, the moments regarded as unknown harmonic loads are also expanded into Fourier series with unknown coefficients, and are included in the equations for the coefficients. The natural frequencies and the mode shapes of the actual membrane or plate are determined by calculating the eigenvalues and the eigenvectors of the equations. The method is applied to circular‐segment‐shaped membranes and plates of rectangular orthotropy, the natural frequencies and the mode shapes of the membranes and plates are calculated numerically, and the effect of the shape and orthotropy is discussed.