We use computer simulation to compares four types ofbuffer allocation strategies in shared buffer ATM switches under CBR load, including complete partition(CP), complete sharing(CS), sharing with minimum allocation(SMA), sharing with maximum queue length(SMXQ). We compare the four strategies from three aspects: cell loss probability(R), mean delay(D) and delay distribution (delay jitter). By the comparison, we find that CPis not good for its large buffer capacity, and CS is not good for its unfairness among the output ports.Because SMA and SMXQ have a trade-off between buffer utilization and fairness, they are good buffer allocation strategies in practical applications.