We have developed a spherical FCT code in order to simulate the interaction of supernova remnants with stellar wind bubbles. We assume that the density profile of the supernova ejecta follows the Chevalier mode1(1982) where the outer portion has a power-law density distribution(ρ∝γ−n ρ∝γ−n ) and the SN ejecta has a kinetic energy of 1051 1051 ergs. The structure of wind bubble has been calculated with the stellar mass loss rate ˙ M=5×10−6M⊙/yr M˙=5×10−6M⊙/yr and the wind velocity υ=2×103 υ=2×103 km/s We have simulated seven models with different initial conditions In the first two models we computed the evolution of SNRs with n=7 and n=14 in the uniform medium The numerical results agree with the Chevalier's similarity solution at early times. When all of the power-law portion of the ejecta is swept up by the reverse shock, the evolution slowly converges to the Sedov-Taylor stage. There is not much difference between the two cases with different n's The other five models simulate SNRs produced inside wind bubbles. In model III, we consider the SN ejecta of 1.4 M⊙ M⊙ and the radius of bubble ~2.76 pc so that ratio of the mass α(=MW.S/Mej α(=MW.S/Mej is 2. We follow the complex hydrodynamic flows produced by the interaction of SN shocks with stellar shocks and with the contact discontinuities, In the model III, the time scale for the SN shock to cross the wind shell τcross τcross is similar to the time scale for the reverse shock to sweep the power-law density profile τbend τbend . Hence the SN shock crosses the wind shell. At late times SN shock produces another shell in the ambient medium so that we have a SNR with double shell structure. From the numerical results of the remaining models, we have found that when τcross/τbend≤2 τcross/τbend≤2 , or equivalently when α≤50 α≤50 , the SNRs produced inside wind bubbles have double shell structure. Otherwise, either the SN shock does not cross the wind shell or even if it crosses at one time, the reverse shock reflected at the center accelerates the wind shell to merge into the SN shock Our results confirm the conclusion of Tenorio-Tagle et a1(1990).