Abstract <p>In the paper, the free vibrations of isotropic prismatic thin shells with a square cross section have been studied. The effect of the length and number of faces on the vibrations of prismatic shells has been analyzed in the preceding studies, where a classification of frequencies has been introduced. The free vibrations were split into the groups: shell-, plate-, and beam-like vibrations. For the case of the square cross section, the estimates for the beam-like frequencies have been obtained. However, plate-like frequencies have not been discussed in detail. In this paper, the plate frequencies and vibration modes of a prismatic shell with a square cross section analyzed out using analytical and numerical methods. A classification of frequencies and vibration modes depending on the boundary conditions on the conjugation lines of the shell faces has been developed. The spectrum frequency distribution depending on the characteristic sizes of the shell and the boundary conditions at its ends has been discussed.</p>