<p><it>Abstract—</it>The mesh-connected computer with multiple buses (MCCMB) is a well-known parallel organization, providing broadcast facilities in each row and each column. In this paper, we propose a 2-D generalized MCCMB (2-GMCCMB) for the purpose of increasing the efficiency of executing some important applications of prefix computations such as solving linear recurrences and tridiagonal systems, etc. A $<tmath>k_1n_1 \times k_1n_2</tmath>$ 2-GMCCMB is constructed from a $<tmath>k_1n_1\times k_1n_2</tmath>$ mesh organization by enhancing the power of each disjoint $<tmath>n_1\times n_2</tmath>$ submesh with multiple buses (sub-2-MCCMB). Given $<tmath>n</tmath>$ data, a prefix computation can be performed in $<tmath>O(n^{1/10})</tmath>$ time on an $<tmath>n^{3/5}\times n^{2/5}</tmath>$ 2-GMCCMB, where each disjoint sub-2-MCCMB is of size $<tmath>n^{1/2}\times n^{3/10}</tmath>$. This time bound is faster than the previous time bound of $<tmath>O(n^{1/8})</tmath>$ for the same computation on an $<tmath>n^{5/8}\times n^{3/8}</tmath>$ 2-MCCMB. Furthermore, the time bound of our parallel prefix algorithm can be further reduced to $<tmath>O(n^{1/11})</tmath>$ if fewer processors are used. Our result can be extended to the $<tmath>d</tmath>$-dimensional GMCCMB, giving a time bound of $<tmath>O(n^{1/(d2^d+d)})</tmath>$ for any constant $<tmath>d</tmath>$; here, we omit the constant factors. This time bound is less than the previous time bound of $<tmath>O(n^{1/(d2^d)})</tmath>$ on the $<tmath>d</tmath>$-dimensional MCCMB.</p><p><it>Index Terms—</it>Broadcasting, mesh-connected computers, mesh-connected computers with multiple buses, parallel algorithms, prefix computation, rectangular meshes.</p>