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In drawing microstructured optical fibers (MOFs), the cross-sectional hole structure, including holes' relative size and shape, in a finished fiber drawn down from a preform can be different from that designed in the preform due to combined effects of draw tension and surface tension. As a result, the fiber's optical properties relative to the initial design can be significantly altered. In order to find means of minimizing or exploiting hole deformation so that MOFs with desirable optical functionality can be fabricated, the underlying mechanism of hole deformation is analyzed by numerically investigating the continuous draw process of MOFs of different materials under different drawing conditions. It is found that three dimensionless numbers, i.e., 1) the capillary number (related to material properties), 2) the draw ratio, and 3) the aspect ratio (both related to the drawing conditions), can be used to predict the type of hole deformation. Silica and polymer materials are considered in particular, but the use of these dimensionless numbers allows the analysis to be applied to any other material.