<p>The main purpose of this work is to present a new trigonometric shear deformation theory (TSDT) in conjunction with the strain-based approach for developing a four-node quadrilateral high-order plate bending finite element with five degrees of freedom per node for bending and buckling analysis of sigmoid functionally graded porous (S-FGP) plates. In this context, a novel shear function is introduced within the framework of a five-unknown high-order shear deformation theory, where the shear strain variation across the plate thickness is nonlinear, with zero transverse shear stress on the upper and lower surfaces. Therefore, the introduction of shear correction factors is not required. The sigmoid law distribution is considered for modeling the material characteristics of plates, which vary gradually in the thickness direction. To describe the internal pores of plates, three porosity distribution types in terms of cosine functions are adopted: symmetrical center-enhanced distribution, bottom-enhanced distribution, and top-enhanced distribution. Comparative studies with published higher-order analytical and numerical models demonstrate the simplicity and efficiency of the proposed model in predicting S-FGP plates under complex mechanical conditions. Moreover, numerical applications of S-FGP plates are conducted to evaluate the impacts of loading type, boundary conditions, porosity coefficient, material index, and geometric parameters on the bending and stability behaviors. In summary, this study provides key insights that enhance the comprehension of the mechanical behavior of porous sigmoid functionally graded plate structures.</p>