Bond lengths - a single bond is 0.153nm while a double bond is 0.134nm, making Kekulé's model of alternating single and double bonds asymmetric. Other evidence shows benzene to be symmetrical so it cannot have this combination. Instead, all bonds are 0.139nm.
Enthalpy change of hydrogenation - if cyclohexene is hydrogenated, the enthalpy change for adding hydrogen across 1 double bond is -120kJ/mol. If benzene has 3 double bonds, it should have an enthalpy change of -360kJ/mol (3x120). However, when benzene is hydrogenated, it releases -208kJ/mol, showing it to be more stable than Kekulé's structure. This supports the theory of a delocalised electron ring as this electronic structure stabilises the molecule.
Resistance to reaction - benzene will not react with halogens or strong acids, or take part in addition reactions so it does not react like an alkene. This suggests that C=C double bonds are not present.