Multitasking on reconfigurable logic can achieve very high silicon reusability. However, configuration latency is a major limitation and it can largely degrade the system performance. One reason is that tasks can run in parallel but configurations of the tasks can be done only in sequence. This work presents a novel configuration model to enable configuration parallelism. It consists of multiple homogeneous tiles and each tile has its own configuration SRAM that can be individually accessed. Thus multiple configuration controllers can load tasks in parallel and more speedups can be achieved.