<p>The main aim of the present study is to develop a meshfree Jacobi-radial point interpolation (Jacobi-RPI) method for the free vibration and stochastic response analyses of laminated composite sectorial and annular plates with straight fibers and variable thickness. The Hamilton’s principle is adopted to establish the equations of motion of the laminated composite sectorial plate with straight fiber and variable thickness in framework of first-order shear deformation theory (FSDT). The straight fibers of the laminated sectorial plate are modeled by introducing fiber angles varying with circumferential coordinate, which leads to the loss of symmetry with respect to the rotation axis of the plate. Therefore, the equations of motion of the laminated annular plate with straight fiber are obtained by combining the equations of the several sectorial plates. The displacement components of the plate are approximated by using the meshfree Jacobi-RPI shape function. The accuracy and reliability of the proposed method are validated through a sufficient number of numerical studies. Finally, the effect of fiber direction, thickness parameter and boundary condition on the free vibration and stochastic response of the laminated composite sectorial and annular plates are discussed.</p>