We propose an adaptive processor allocation strategy based on shape manipulations of required submesh for large mesh-connected systems. When an incoming job requests a rectangular submesh, our strategy first tries to allocate the conventional rectangular submeshes including 90-degree rotation and folding techniques. If it fails, our strategy further tries to allocate more flexible and robust L-shaped submeshes instead of signaling the allocation failure. Thus, our strategy accommodates incoming job earlier than conventional strategies. Simulation results indicate that our strategy performs more efficiently than other strategies in terms of the external fragmentation, the job response time, and the system utilization. Our strategy is transparent to application programmers and does not require additional hardware supports. Moreover, with our L-shaped submesh allocation strategy, application programmers using the mesh-connected system may no longer limit their request to rectangular submeshes. They can request the L-shaped submesh with the number of processors much closer to the exactly needed value to execute their job.