A method of modifying a polyethylene is disclosed. In the method ethylene or a mixture of ethylene and a C3-C10 .alpha.-olefin is polymerized in an organic solvent with a Ziegler or single-site catalyst to form an initial polyethylene solution. The initial polyethylene solution is then reacted with a free radical initiator to produce a modified polyethylene. The modified polymer has an enhanced melt elasticity and increased long chain branching index, and is essentially free of gel.