From the existing literature, several variants of the differential equation solution of transverse vibrations of a plate, including approximate methods (variational methods of Ritz and Galerkin, Rayleigh, Leibenson, and numerous other scientists), are noted. In several cases, scientists proposed equations of the vibration form of a homogeneous plate that is satisfied when these equations are fulfilled. Thus, the solution is reduced to the Bessel equation (the first and second type). Several researchers investigated differential equation solutions in the form of a series (proposed in due time by Timoshenko, Theory of oscillations in engineering ONTI 1934, and by Cato Kenza, Iap. Soc.Mech.Eng.41.N: 347.1975. 1996-2000 c). At the end of the 20th century, theories on the functions of a complex variable and conformal mapping (Guz, Kubenko V.D, Aleksandrovich, Kosmodamiansky, etc.) were applied. By using the above method of inputting the function of a complex variable and conformal mapping, the oscillation problem of a polygonal plate was solved, and the solution was published in Moscow in the journal Izvestiya Rossiiskoi Akademii Nauk. Here, we propose a different approach for solving the oscillation problem of a polygonal, in which a connected plate was multiplied using rectilinear cuts.