Several renumbering strategies for unstructured grids are discussed. They lead to a minimization of eache‐misses and an optimal grouping of elements for different computer platforms, from superscalar workstations to multiprocessor register‐to‐register vector machines. Timings for a typical computational fluid dynamics (CFD) code that employs these renumbering strategies indicate that CPU requirements may be halved by applying them. The renumbering strategies discussed are all of linear time complexity, making them ideally suited for applications requiring frequent mesh changes. Furthermore, these renumbering strategies are not only valid for element‐based codes but carry over to edge‐based or face‐based field solvers.