CADY is a cell-penetrating peptide spontaneously making non-covalent complexes with Short interfering RNAs (siRNAs) in water. Neither the structure of CADY nor that of the complexes is resolved. We have calculated and analyzed 3D models of CADY and of the non-covalent CADY-siRNA complexes in order to understand their formation and stabilization. Data from the ab initio calculations and molecular dynamics support that, in agreement with the experimental data, CADY is a polymorphic peptide partly helical. Taking into consideration the polymorphism of CADY, we calculated and compared several complexes with peptide/siRNA ratios of up to 40. Four complexes were run by using molecular dynamics. The initial binding of CADYs is essentially due to the electrostatic interactions of the arginines with siRNA phosphates. Due to a repetitive arginine motif (XLWR(K)) in CADY and to the numerous phosphate moieties in the siRNA, CADYs can adopt multiple positions at the siRNA surface leading to numerous possibilities of complexes. Nevertheless, several complex properties are common: an average of 14±1 CADYs is required to saturate a siRNA as compared to the 12±2 CADYs experimentally described. The 40 CADYs/siRNA that is the optimal ratio for vector stability always corresponds to two layers of CADYs per siRNA. When siRNA is covered by the first layer of CADYs, the peptides still bind despite the electrostatic repulsion. The peptide cage is stabilized by hydrophobic CADY-CADY contacts thanks to CADY polymorphism. The analysis demonstrates that the hydrophobicity, the presence of several positive charges and the disorder of CADY are mandatory to make stable the CADY-siRNA complexes.