The analysis of static bending and free and forced vibration responses of functionally graded fluid-infiltrated porous (FGFP) skew and elliptical nanoplates placed on Pasternak’s two-parameter elastic foundation is performed for the first time using isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBSs) basis function. Three types of porosity distributions affect the mechanical characteristics of materials: symmetric distribution, upper asymmetric distribution, and lower asymmetric distribution. The stress–strain relationship for Biot porous materials was determined using the elastic theory. The general equations of motion of the nanoplates were established using the four-unknown shear deformation plate theory in conjunction with the nonlocal elastic theory and Hamilton’s principle. A computer program that uses IGA to determine the static bending and free and forced vibration of a nanoplate was developed on MATLAB software platform. The accuracy of the computational program was validated via numerical comparison with confidence assertions. This set of programs presents the influence of the following parameters on the static bending and free and forced vibrations of nanoplates: porosity distribution law, porosity coefficient and geometrical parameters, elastic foundation, deviation angle, nonlocal coefficient, different boundary conditions, and Skempton coefficients. The numerical findings demonstrated the uniqueness of the FGFP plate’s behavior when the porosities are saturated with liquid compared with the case without liquid. The findings of this study have significant implications for engineers involved in the design and fabrication of the aforementioned type of structures. Furthermore, this can form the basis for future research on the mechanical responses of the structures.