Abstract The critical local buckling of simply-supported sinusoidal panels subjected to uniaxial compression using the Rayleigh-Ritz method is investigated. With increased applications of thin-walled composite structures in engineering, these corrugated panels are especially popular due to their high stiffness to weight ratio and high out-of-plane rigidities. Failure of such thin-walled panels occurs mainly in buckling rather than material failure; thus, it leads to the importance of buckling failure analysis. Conventional methods are limited when analyzing these panels in local buckling because of its unique geometries. Hence, a semi-analytical solution is developed to predict the local buckling based on classical shell theory with a unit cell approach, and it shows excellent correlation with the results based on the numerical finite element analysis . A parametric study is conducted to evaluate the effects of the thickness, aspect ratio, and the corrugated amplitude of the panel on buckling. It is revealed that the derived solution can accurately capture the local buckling behavior at high thickness/radius of curvature ratios, any aspect ratios, and high corrugated amplitudes. Additionally, the effects of orthotropy, Poisson’s ratios and twisting capacities on the buckling behavior are explored. The proposed semi-analytical solution can be effectively used to aid in the efficient and accurate design analysis and optimization of corrugated panels.