-  Ice flow over a Snowball ocean was shown in recent years to be capable of very effectively homogenizing ice thickness globally. Previous studies all used local or one-dimensional global (latitude-only) models, formulated in a way that is difficult to extend to two-dimensional global configuration. This paper uses a two-dimensional global ice flow model to study the effects of continental constriction on ice flow and ice thickness in a Snowball-Earth scenario using reconstructed Neoproterozoic landmass configuration. Numerical simulations and scaling arguments are used to show that various configurations of continents and marginal seas which are not represented by one dimensional models lead to large ice thickness variations, including narrow areas between sub-continents and marginal seas whose entrance is constricted. This study ignores many known important factors such as thermodynamic, optical effects, dust and dust transport, and is therefore meant as a process study focusing on one specific effect, rather than a realistic simulation of Neoproterozoic ice thickness. The model formulation developed here generalizes and extends previous results in several ways, including the introduction of corrections due to spherical coordinates and lateral geometry. This study is therefore a step toward coupling Snowball ice flow models to general circulation ocean and atmospheric models and allowing a more quantitative simulation of Neoproterozoic Snowball ice thickness.