The residue-residue contacts contribute more function to the protein folding and play an active role in the stability of proteins．we calculate the number of medium-and long-range contacts for 90 (α/β)8 barrel proteins with considering the distance between the centers of two residues in defining residue-residue contacts．The ability to forming contacts in each (α/β)8 barrel protein was discussed through calculating the number of long- and medium- ranges contacts for different residues in proteins．The relationship between the average numbers of medium-and long-range contacts with Fauchere-Pliska hydrophobicity value (FPH) for 20 amino acid residues was studied

and it was found that the average number of long-range contacts had a linear relation with the Fauchere-Pliska hydrophobicity value (FPH)

however

it had not valid for medium-range contacts．The dimension of (α/β)8 barrel proteins has a good relation to the long-range contact of proteins

and the characteristic ratio of mean-square radius of gyration 〈S2〉 can be expressed as 〈S2〉／N=a′+b′×LRO is where LRO is the long-range order

N is the number of residues

and a′=2.32

b′=-0.131．When a protein has a large LRO value

the structure is compact and it has a small dimension value. These investigations can provide some insights into structure of (α/β)8 the barrel proteins．