Fluted-core sandwich composites have a promising prospect in lightweight engineering applications due to their superior strength-to-weight ratio. Herein, trapezoidal fluted-core sandwich composite cylinders made of carbon fiber-reinforced plastics were designed and integrally fabricated to improve the deformation stability. The effects of circumferential cell number and wall thickness on the bearing characteristics and failure mechanism were assessed by quasi-static uniaxial compression and finite element analysis (FEA). The results revealed that local buckling was likely to appear in sandwich cylinders with small number of cells, leading to undesirable bearing capacity and inferior material utilization. Increasing the cell number and wall thickness could effectively improve the critical local buckling load. Considering the lightweight design requirements, the specific buckling load could be enhanced by increasing the core-rib to facesheet thickness ratio. Nevertheless, with the increase of the thickness ratio, the specific peak force increased rapidly first and then was almost saturated. Furthermore, an analytical approach with high computational efficiency was employed to predict the critical local buckling load. The theoretical predictions agreed well with the FEA results for the cylinders with large number of cells. Compared to other published composite cylindrical shells, the typical specimen fabricated in this study exhibited the highest specific peak force (563.4 kN/kg) and superior specific compressive strength (37.98 MPa/kg), demonstrating great application potential for large-size and lightweight launch-vehicle shell structures.