We need an enormous amount of memories for name spaces as well as additional processors if we are to effectively exploit a massively parallelism in nested loops of functional languages such as Id. If there is no sufficient amount of memories enough to exploit that parallelism, the execution of programs can be aborted during the unfolding of loops. Additionally, if loops are overunfolded, compared with the number of processors available, the system performance can be degraded severely due to the overhead of loop unfolding. This paper suggests and analyzes an algorithm which can be used to effectively unfold nested loops of functional languages on multithreaded architectures. This algorithm has a feature to unfold a given nested loop safely and near optimally, considering the system resources of processors and memories available when the loop is to be unfolded.