A model with solution viscoelasticity is proposed to explain the ratchetlike stretching of DNA by a symmetric ac electric field in polymer solutions. In this model, DNA is stretched by the interaction between the fluid elasticity and the oscillatory flow induced by DNA. Predictions of the model are confirmed by DNA stretching experiments performed in various polymer solutions and the corresponding rheological measurements of the solutions. In particular, experiments have verified that a net migration of stretched DNA in polymer solutions can be induced by a zero-mean asymmetric ac electric field. This last finding cannot be explained by other existing models.