We present efficient parallel algorithms for the maximum empty rectangle problem in this paper. On crew pram, we solve the area version of this problem inO(log2n) time usingO(nlogn) processors. The perimeter version of this problem is solved inO(logn) time usingO(nlog2n) processors. On erew pram, we solve both the problems inO(logn) time usingO(n2/logn) processors. We also present anO(logn) time algorithm on a mesh-of-trees architecture.