The side–side, side–tip, and tip–tip clumping of nanofibers, including nanowires and nanotubes on surfaces, is a common problem that can diminish their optical, electrical, and mechanical performance. However, these different clumping configurations brought much complexity and confused researchers to predict or design the desired clumping or nonclumping. In this study, a universal model in the unified formula for the critical clumping criteria for three contact geometries of nanofiber arrays is derived in terms of two-dimensionless geometric and mechanical parameters, based on the length, radius, spacing, Young's modulus, and adhesion energy of the nanofibers. The model provides an easy way to predict the sequences of the three clumping configurations, which are successfully verified by analyzing various clumping structures reported in the literatures. This study provides new insights into, and methods for, designing nanofiber arrays on surfaces to achieve desired clumping or nonclumping structures.