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Venus’s induced magnetosphere is characterized by regions with different plasma and magnetic field properties, which are separated by plasma boundaries. These boundaries’ locations and shapes vary with upstream solar wind conditions, and these variations have been characterized by several previous studies. In this study, we developed quantitative parametric models of the bow shock and ion composition boundary (ICB), which allow us to determine the location and shape of the boundaries given a set of upstream conditions. To quantitatively model these boundaries, we used a database of boundary crossings derived from plasma and magnetic field measurements by Venus Express. We modeled the bow shock as a conic section curve, which depends on the interplanetary magnetic field (IMF) magnitude and the solar wind proton flux. Furthermore, we considered the shock normal angle, the angle between the IMF and the local shock normal vector, to describe a quasi-perpendicular/quasi-parallel shock asymmetry. We modeled the dayside ICB as a half sphere that depends solely on the solar EUV flux and the solar wind proton flux. These parametric models are compared with models that average over upstream conditions; our bow shock parametric model improves the prediction accuracy by 16% and the ICB parametric model by 6%.