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Microstructured optical fibers (MOFs) achieve their desired performance via a pattern of holes that run along the length of the fiber. Varying the hole pattern allows a variety of optical effects to be produced. However, the original hole pattern within the preform may not be accurately transferred to the finished fiber due to the combined impact of material properties and the drawing conditions experienced during fabrication. In this two-part paper, the processes of drawing MOFs having arbitrary cross-sectional hole structures will be analyzed for the case of Newtonian materials. Part I presents a modeling formalism to describe the drawing processes, followed by a scaling analysis on a representative case, i.e., the nonisothermal drawing of an axisymmetric annular hollow fiber, to reveal the major factors influencing the drawing of both silica and polymer MOFs. By treating the primary draw process (i.e., from preform to intermediate cane) in fabricating polymer MOFs as a transient, isothermal problem, numerical simulations were carried out for an illustrative five-hole structure. The results revealed the central importance of any steep neck-down region on hole-shape deformation as well as the importance of forces additional to those associated with surface tension effects. Both experimental observations and numerical modeling show that a diversity of hole "activities" (both in a hole's relative size and shape) can occur when drawing MOFs. Part II will extend both the analysis and numerical modeling with a focus on the steady-state continuous draw process (i.e., from preform or cane to fiber). In parallel with this analysis, we also present experimental results for the drawing of polymethylmethacrylate (PMMA) MOFs.