Free vibrations of a thin prismatic isotropic shell with rectangular cross-section are studied in the paper. The behavior of lower part of the vibration frequencies’ and modes’ spectrum is studied for the isoperimetric problem, when cross-section is changed from square to rectangular while its perimeter is preserved. Previously a vibration problem for the prismatic shell with square cross-section was studied, and vibration modes classification, which is related to the shell side edges' boundary conditions, was obtained. In this report, the behavior of vibration modes and frequencies upon changing cross-section from square to rectangular is analyzed, and the connection between the shell frequencies and partial plate frequencies is described.