<p>The Ritz method is highly effective for analysing various structural elements, including plates, shells, panels, and frames. However, its use in analysing functionally graded porous curved (FGPC) beams remains relatively insufficiently explored. This paper presents a novel approach utilising Laguerre functions-based Ritz method to examine the bending, buckling, and free vibration characteristics of FGPC beams. A higher-order shear deformation theory is adopted to accurately model the displacement field pertinent to the problem. Lagrange’s equations are employed to derive the governing equations of motion. The investigation encompasses FGPC beams subjected to three distinct boundary conditions and incorporates two types of porosity distributions. Numerical examples are conducted to evaluate the proposed methodology’s accuracy and efficiency. Moreover, the study meticulously explores the effects of slenderness ratio, boundary condition, porosity distribution, porosity ratio, power-law index, and curvature on the bending, buckling, and vibrational responses of FGPC beams, providing comprehensive analyses and discussions. The results indicate that the methodology proposed herein is straightforward and effective for comprehensively analysing FGPC beams. Furthermore, the boundary condition and the porosity factor significantly impact the bending, buckling, and vibration behaviours of FGPC beams. This research yields several innovative findings that establish a benchmark for subsequent investigations. Additionally, the outcomes of this study enhance the safe and efficient design of engineering systems that integrate FGPC structures.</p>