This paper investigates the optimal configurations of composite grid-stiffened cylindrical panels for buckling and free vibration, using a semi-analytical method. The formulations are based on the classical Kirchhoff-Love assumptions and the Extended Kantorovich Method (EKM) is applied to solve the governing system of partial differential equations (PDEs). Using the EKM, the governing PDEs convert into a double set of ordinary differential equations ODEs. Semi‐analytical solutions are presented for both buckling and free vibration of the panels via iterative application of infinite power series solution for the sets of ODEs. Various lattice unit cell configurations including lozenge, kagome, diamond, triangle, rectangle, and honeycomb unit cells are developed for the panel subject to clamped boundary conditions. The angle of ribs, their dimension, and numbers in a unit cell are considered as design variables and the optimal unit cell is introduced in terms of critical buckling loads and natural frequencies. Since the rectangular plate PDEs are available by making some geometrical changes in the equations of the panel, the study is also performed similarly for plates.