A 3D Reynolds-averaged Navier-Stokes (RANS) model was refined in the paper based on the turbulence model to simulate the drag reduction (DR) flow in the tube. The influence of elastic parameters on the drag reduction effect was studied using this numerical model and validated by the DNS data. The results showed that DR effect increased with both the relaxation time λ and the maximum extensibility of molecule L . DR effect had an upper limit with the increasing of the maximum extensibility of molecule L . and the growth of relaxation time λ also could enhance that upper limit.