The article is devoted to the asymptotic derivation of two-dimensional equations of membrane shells of the von Kármán's type by the asymptotic expansion of a three-dimensional model of a nonlinear elastic membrane shell made of Saint-Venant-Kirchhoff material for the case when only part of the side face of the shell is subject to boundary conditions of a special type. It is known that the von Kármán's model is widely used in numerical calculations, but, at the same time, it is a purely technical simplification in the theory of plates and shells that does not have proper physical justification. Therefore, many works are devoted to determining such restrictions on the geometry of shells and the nature of the forces applied to them, which allow the use of the von Kármán's model. The asymptotic expansion presented in the work completely repeats the earlier material of \textit{B. Miara} [Arch. Ration. Mech. Anal. 142, No. 4, 331--353 (1998; Zbl 0906.73041)] and other cited authors. The analysis of references covers mainly the period up to 2015, only 6 out of 34 sources are younger than 9 years, while 4 of the latter are self-citations. The goal stated in the introduction ``to derive two-dimensional models of membrane shells with boundary conditions of von Kármán's type, which extends that derived by Miara \dots for membrane shells'' is not explicitly shown in the main material of the article and information about achieving this purpose is absent in the conclusions. The results stated in the conclusions ``We found in particular that the forces of von Kármán's type should be of order $O(\varepsilon^0)$'' are physically insignificant. From a mathematical point of view, this only means that when solving the equations of the von Kármán's model by asymptotic methods, the main term in the expansion of forces in the small parameter of the shell thickness must be taken as a constant. The conclusion about the inapplicability of the Airy function is like that obtained in the earlier work of \textit{P. G. Ciarlet} and \textit{L. Gratie} [J. Math. Pures Appl. (9) 80, No. 3, 263--279 (2001; Zbl 1055.35051)], where the conclusion is ``it seems unlikely that the boundary conditions on the Airy function could still be determined along the entire boundary \dots \ solely from the data of the three-dimensional problem.'' A statement about planning a study of the G-convergence of the von Kármán's model is not a conclusion itself. However, it is unclear how the planned study will be better than the already conducted one, for example, in the cited work by \textit{M. Lewicka} et al. [Arch. Ration. Mech. Anal. 200, No. 3, 1023--1050 (2011; Zbl 1291.74130)]. Thus, the article under review may be of interest to those researchers who see value in further asymptotic research into the justification of the von Kármán's model