A theoretical calculation on the sol fraction of the cross-linked long-chain polymers is given． It is based on the following three assumptions：1)that gel is an infinite network；2)that either units of sol or units of gel are cross—linked with equal probability；3)that the cross-linking process within a molecule (cyclization) occurs in gel，but may be neglected in sol．By using two independent methods，namely，the direct summation of infinite series and the probability derivation，the sol fraction formula of cross-linked high polymer produced from initial linear polymer obeying an arbitrary distribution is obtained．Vari-ous special cases are discussed．