This paper shows how to parallelize tree-structured computations ford-dimensional (d ≥ 1) mesh-connected arrays of processors. A tree-structured computationTconsists ofncomputational tasks whose dependencies form a task treeTofnconstant degree nodes. Each task can be executed in unit time, and sends one value to its parent task after it has executed. Lethbe the height ofT. We present linear time algorithms for partitioning and mapping the task treeTonto ap1/d × … × p1/dmesh-connected array of processors so that we can schedule the processors to perform computationTinO(n/p) time, forp ≤ min{n/h,nd/(d + 1)}. TheO(max{h,n1/(d+1)}) time bound achieved whenp = min{n/h,nd/(d + 1)} is the best possible (upto a constant factor) over allp ≥ 1. The best previous bound wasO((√n + h) · logn) achieved on a linear array of min{n/h,n1/2} processors, and could not be generalized to higher dimensional meshes. As a consequence, we obtain a mapping and schedule of ann-node expression tree of associative operators over ap1/d × … × p1/dmesh-connected processor array, which evaluates the expression tree inO(n/p) time, forp ≤ nd/(d + 1)