•The 450/-450/-450/450 clamped shell with y – stiffener should be preferred.•The shells must have nx = 0, ny = 7 stiffeners below the mid-surface.•The clamped shells must have stiffeners satisfying dst/h = 8.•The nonlinear approach for stiffened shells is must to get correct predictions. The non-dimensional fundamental frequencies and mode shapes of laminated composite singly curved stiffened shells are studied in this paper for varying boundary condition, lamination and stiffener properties like orientations, eccentricities, numbers and depth. An isoparametric C0 continuous finite element code combining von-Karman nonlinearity and Sanders’ first approximation theory is proposed here. The curved surfaces are formulated by nonlinear strains while the stiffeners adopted both geometrically linear and nonlinear strains. Correctness of the proposed approach is confirmed through solutions of benchmark problems. The results are critically discussed, and it is concluded that the clamped 450/-450/-450/450 shell with y - stiffeners (nx = 0, ny = 7) located below the mid-surface shows the greatest fundamental frequencies. This study concludes that the nonlinear approach is essential for both shell and stiffener for correct predictions of natural frequencies and mode shapes. The relatively simpler linear approach can be considered for shells having single x – stiffener only.