In patient-specific arterial fluid-structure interaction computations the image-based arterial geometry does not come from a zero-stress state (ZSS), requiring an estimation of the ZSS. A method for estimation of element-based ZSS (EBZSS) was introduced earlier in the context of finite element wall discretization. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the “opening angle.” 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we introduce the version of the EBZSS estimation method with isogeometric wall discretization. With NURBS basis functions, we may be able to use larger elements, consequently less number of elements, compared to linear basis functions. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we present 2D test computations with straight-tube configurations.