This research paper presents a new contiguous allocation strategy for 3D mesh-connected multicomputers. The proposed strategy maintains a list of maximal free sub-meshes and gives priority to allocating corner and boundary free sub-meshes. The goal of corner and boundary allocation is to decrease the number of leftover free sub-meshes and increase their sizes, which is expected to reduce processor fragmentation and improve overall system performance. The proposed strategy, which is referred to as Turning Corner-Boundary Free List (TCBFL) strategy, is compared, using extensive simulation experiments, to several existing allocation strategies for 3D meshes. These are the First-Fit (FF), Turning First-Fit Free List (TFFFL), and Turning Busy List (TBL) allocation strategies. The simulation results show that TCBFL produces average turnaround times and mean system utilization values that are superior to those of previous strategies.