<p>This paper proposes a numerical solution method to analyze free vibration of individual and coupled shells of revolution made by functionally graded porous (FGP) materials by introducing Walsh series method (WSM). The shell structures considered in this paper include conical, cylindrical, spherical shell, coupled conical-cylindrical shell (CCCS), coupled spherical-cylindrical shell (CSCS), and coupled conical-cylindrical-spherical shell (CCCSS). The coupled structure consists of individual shells constructed from identical FGP materials, and the artificial spring technique is used for each shell to be coupled elastically. It is possible to derive the displacements of the shell structures from the first-order shear deformation theory (FSDT). The introduction of Walsh series makes it possible to transform the differential equations that describes the motion of the shell structures, into the discretized algebraic equation and they can be one of the standard linear eigenvalue problems. To demonstrate the accuracy and convergence of the proposed method, it is possible to compare the results obtained from the proposed method with those from the ABAQUS software using the finite element method (FEM) and the findings in previously published related literature. Through the final results, it is proved that this WSM converges rapidly and there hardly exists difference between the results of WSM and the data of previous published literature or the results of the FEM. At the end of the paper, the various parametric studies of the coupled shell structures with the variation of the geometric dimension and the variation of the porosity coefficient of the FGP material are investigated and reported.</p>