A rubber composition comprises at least one phenol/aldehyde resin based on at least one aromatic polyphenol comprising at least one aromatic ring bearing at least two hydroxyl functions in the meta position relative to one another, the two positions ortho to at least one of the hydroxyl functions being unsubstituted, and at least one aromatic polyaldehyde selected from 1,3-benzenedicarboxaldehyde, 1,4-benzenedicarboxaldehyde and mixtures of these compounds, the rubber composition having a nominal secant modulus at 10% elongation, measured according to standard ASTM D 412, 1998, of greater than or equal to 25 MPa.