Relevance. Sector plates are used as components of drill bits in the oil and gas industry. In order to design strong, wear-resistant structures that are as light as possible, it is necessary to use functional-gradient materials – composites that significantly increase the reliability and efficiency of equipment in the oil and gas industry. Aim. To investigate the stress-strain state of drill bit elements under loads of different intensities. To achieve this, a mathematical model must be built. To develop the methods of analysing functional-gradient, size-dependent sector plates of drill bit elements. To analyze the main factors affecting the stress-strain state of the considered structures. Methods. This paper introduces a fast, enhanced variational iteration method, which enables us to obtain a practically exact solution. This method is based on the idea of Fourier separation of variables and an iterative process that reduces nonlinear partial derivative equations to ordinary differential equations. Results. The authors constructed a new mathematical model of porous, Kirchhoff-type, functionally graded, sectoral macro/micro plates, considering nonlinearity according to T. von Kármán. The paper introduces the effective method in terms of accuracy and speed – the variational iteration method. The stress-strain state of sector plates is analysed depending on plate geometry, type of nonlinearity, porosity, and dimensions.