Abstract: In the numerical simulations of compressible reacting flow with detailed reaction mechanism, the computations of chemical source term can spend huge CPU time. A chemistry acceleration algorithm based on tabulation technique can greatly improve the computational efficiency, through replacing the direct computation of chemical reaction by searching the data in a table. However, excessive growth of the table size can give rise to a breakoff of the computations. This study presented the parallel dynamic storage/deletion algorithm based on two table size control strategies. To test the computational performance of the algorithm, the simulations of flame interface instability induced by a shock wave have been carried out. Both table size control strategies in the algorithm include the single table size (M_sin) control and the total table size (M_tot) control. Once the size of single table reached M_sin or the total size of the tables reached M_tot, a nodal deletion was performed for all the tables in order to maintain the table size. The results show that there exists relationship between computational accuracy and efficiency for the algorithm based on the table size control. The better computational efficiency corresponds to the higher computational accuracy. The chemical speedup ratio resulted from simulations ranges in 2.73~3.93 when M_sin and M_tot vary. The combination of both table size control strategies plays an important role in affecting the deletion frequency of tables and the synchronization among the table deletion events. The chemical speedup ratio is larger when smaller deletion frequency of tables and better synchronization occur.