MASC (for Multiple Associative Computing) is a joint control parallel, data parallel model that provides a practical, highly scalable model that naturally supports small to massive parallelism and a wide range of applications. In this paper, we present efficient algorithms for a MASC model with a 2-D mesh to simulate enhanced meshes. Let MASC(n, j) denote a MASC model with n processing elements and j instruction streams. It is shown that a MASC(n, j) model with a 2-D mesh is strictly more powerful than a √n × √n MMB (Mesh with Multiple Broadcasting) when j =Ω(√n ). Simulation of a √n × √n MMB by MASC(n, j) with a 2-D mesh runs in O(1) time and requires no extra memory. Simulating a √n × √n BRM (Basic Reconfigurable Mesh) with MASC(n, j) with a 2-D mesh takes O(√n) extra time with O(n) extra memory when j =Ω(√n ). The reverse simulations of MMB or BRM with MASC with a 2-D mesh is also given. These simulations not only provide information about the power of the MASC model and also provide an automatic conversion of numerous algorithms designed for enhanced meshes to the MASC model.