We propose and evaluate a new processor allocation strategy in two-dimensional Multicomputers. The proposed strategy is comparatively evaluated against a set of well-known allocation strategies from the literature, namely; the 2D buddy System (Juang et al., 1997), the Multiple Buddy System and the Paging non-contiguous processor allocation strategies. Our experimental results show that the proposed allocation strategy has solved a number of flaws and drawbacks that have been observed in previously proposed strategies. Further, we observed that our proposed allocation strategy is scalable. We refer to the newly proposed strategy by the "Flexible 2D Buddy System" or F2DBS for short. In our experimental results, we also demonstrated that the F2DBS strategy is more flexible and applies to any 2D mesh of any shape and orientation.